How to build a budget-friendly manabase for a 5-color deck?
Here are the lands that will work in a 5 colour deck, I ordered them in roughly the order I think they are helpful speed wise to an EDH deck and will include the lands you already run for completeness. Prices rounded to the nearest quarter and are from TCGPlayer based on the results returned by Scryfall. (For sake of site rules, I have no affiliation with either site)
Without knowing your budget, I can't really limit myself to that budget, but I will give a more general overview of less expensive lands and cycles for 5 colour EDH.
Bond Lands
You're building EDH, a multiplayer free for all format, and bond lands care about how many opponents you have, allied colors being released in Battlebond, the 2HG set, and enemy colors in Commander Legends. Their prices range from Spectator Seating (/) at $5.75 to Morphic Pool (/) at $28.25. These are all but guaranteed to come out in EDH untapped, until the game is almost over when one land drop won't matter so much anymore.
Shock Lands
These have always been an EDH staple, having the basic land types to allow them to be found by some effects (Farseek) and being able to choose to let them come in tapped when the cost (2 life) was not worth it. These were at one time more expensive lands, however with the two further visits to Ravnica each having full reprints of the cycles, the price to get ahold of these lands has gone down quite a bit, they now run from Hallowed Fountain (/) at $7.75 to Breeding Pool (/) at $20.
Filter Lands
There are a few cycles of filter lands, The first cycle from Odyssey requires you to pay 1 mana of any colour to get 2 mana of specific allied colour pairs, cost wise they range from Sungrass Prairie () at $0.25 to Shadowblood Ridge () at $0.50.
The second cycle came out in Llorwyn block, it requires you to spend one mana of the colours it can produce to get two mana in any combination of those two colours. Recent reprints in masters sets have brought this cycle down in price, from Graven Cairns () at $4.25 to Sunken Ruins () at $18. Unlike the Llorwyn cycle, the Odyssey cycle cannot tap for mana without paying into it, the Llorwyn cards have tap for colorless.
Also worth mentioning here is Crystal Quarry () which filters 5 mana into one of each color for $6.75 and Cascading Cataracts for $4.75 which turns 5 mana into 5 mana of any color combination you want.
Pain Lands
These lands tap for colorless, or one of two colors if you pay one life. These lands run in cost from Llanowar Wastes (/) at $0.75 to Adarkar Wastes (/) at $8.75.
Mana Confluence ($20.75) and City of Brass ($16.25) can also be considered here, as they tap for 1 of any colour at the cost of one life, with slightly different wording (cost/vs damage effect). Murmuring Bosk ($1.25) can also be included here, it is a forest so taps for , but can alternatively tap for  or  for 1 life, it will come in untapped if you reveal a treefolk card from your hand. All of these cards, other than City of Brass cannot be used for coloured mana if you are prevented from paying life (effects like Angel of Jubilation or Platinum Emperion) however preventing damage from City of Brass does not prevent it from being used.
Pathway Lands
Zendikar Rising introduced a partial cycle of 6 lands in 2 allied and 4 enemy colour pairs and Kaldheim finished the set with the other 4 pairs. These lands tap for one colour, but when you play them you choose which side enters face up, and thus which of the two possible colours they can tap for. They run from Cragcrown Pathway/Timbercrown Pathway (/) for $2.75 to Darkbore Pathway/Slitherbore Pathway (/) for $5.75. Note if they enter the battlefield in some way other than being played (being flickered or Scapeshift perhaps) they enter with the front face up, no choice about side.
Check Lands
These check that you have one land of the matching colour basic land subtypes out on the field and come in untapped if you do, they don't care if they are basic so Shock, Battle and Bicycle lands will work for this also. Price wise they range from Sunpetal Grove (/) at $3 to Hinterland Harbor (/) at $7.
Reveal Lands
These lands come in untapped if you can reveal a land from your hand with a matching basic type, though it does not need to be basic, so Shock, Battle and Bicycle lands will work. Price wise these go from Fortified Village (/) at $2.25 to Choked Estuary (/) at $3.75.
Battle Lands
These come out untapped if you have at least two basic lands in play, though this makes it less and less likely you will get them untapped the more non-basics you have in your deck, these do unfortunately only exist in allied colours and the costs run from Prairie Stream (/) at $0.75 to Canopy Vista (/) at $2.25. These also have the basic land types, so they will matter for other land types listed, like Check and Reveal lands.
Fast lands
These come out untapped if you have 2 or less other lands can conditionally be faster. They run from Concealed Courtyard (/) at $2.75 to Blackcleave Cliffs (/) at $16.25. These are a little less useful in EDH due to the game format being longer, the deck size larger and the lands limited to one each, the likelihood they will come in untapped is low, they are much better in formats like modern where early advantage means more.
Tainted Lands
These lands tap for colorless, unless you have a swamp, if you do they tap for  or one other color. They go from Tainted Field (/) at $0.25 to Tainted Peak (/) at $4.25. This is a cycle of 4 lands, as the 5th land would be / if you control a swamp, and be a strictly worse than a swamp itself. These also do not care about the land being basic, so Shock, Battle and Bicycle swamps all apply, as do all lands turned into swamps by an effect like Urborg, Tomb of Yawgmoth.
Thriving Lands
Jumpstart added a new cycle of lands, 5 lands that come in tapped, one for each colour of mana. The up side to these lands is they let you pick the other colour they can tap for as you play them. While they do come in tapped and are slower than most of the rest here, the guarantee of giving you the colour you need as your 5th land can mean a lot. They run from Thriving Bluff () at $0.50 to Thriving Isle () at $1.75.
Vivid Lands
Vivid lands always come in tapped, but tapped status really only slows you down if it is the 5th land, completing the set of colors. The major benefit of Vivid lands is they come in with two charge counters, allowing the land to be used for any color twice. They run from Vivid Grove () at $0.25 to Vivid Marsh () at $1.50.
Triomes
Triomes, or tricycle lands (tri color lands with cycling), are an evolution of Bicycle lands seen below. There are 5 lands (half cycle) with a pair of allied colours and their mutual enemy (Khans of Tarkir colors). They come in tapped, but because they have three basic land types they are easy to find and synergize with many of the other effects. They run from Indatha Triome (//) at $5.50 to Zagoth Triome (//) at $10.
Bicycle Lands
These lands will come in tapped, however I am mentioning them because they synergize with Check lands if played earlier and Reveal lands if in the hand. They range in price from Irrigated Farmland (/) at $0.25 to Fetid Pools (/) at $3.75.
Slow Lands
These lands you can only tap once every other turn and come in untapped, there are two cycles, both ally coloured only. The first uses a counter put on when tapping for mana that is removed instead of untapping. These run from Timberline Ridge (/) at $2.95 to River Delta (/) at $4.25.
The other cycle is actually two cycles of 5 which are functional reprints of eachother, all less than $0.25 from Rootwater Depths (/) to Cinder Marsh (/), these can tap for colorless without staying tapped, and use more familiar &quot;does not untap&quot; language.
Other Lands
There are lands that make colours conditionally that could be useful in your deck, like Reflecting Pool ($22) and Exotic Orchard ($0.50) making mana based on what colours you, or your opponents could make. Spire of Industry ($1) costs one life and needs you to have an artifact to make any coloured mana and Glimmervoid ($2.50) makes 1 mana of any colour but is sacrificed if you have no artifacts in play, Thran Quarry ($6.50) works the same but needs creatures. Aether Hub ($0.25) costs one energy to make any coloured mana and Forbidden Orchard ($20) which gives opponents a 1/1 creature for every mana you make with it, but makes any colour. Holdout Settlement ($0.25) and Survivors&#39; Encampment ($0.25) both need you to tap a creature to make coloured mana.
A little less useful cards that make multiple but not any colour, River of Tears ($2) makes  before you play a land for turn or  after. Nimbus Maze ($4.50) can tap for  if you control an island and  if you control a plains, giving you the opposite once you have the other colour's basic land type. Grove of the Burnwillows ($4.25) taps for  or  but gives one life to each enemy, something that rarely matters in EDH where overwhelming damage, poison, commander damage and mill are the usual ways of winning.
Other lands restrict how mana can be spent, but without knowing the deck type can't really be suggested. If it's eldrazi(with devoid) there's Corrupted Crossroads ($0.25), allies have Ally Encampment ($0.25), creature heavy decks can make use of Ancient Ziggurat ($4), dragons have Haven of the Spirit Dragon ($2.75), elementals use Primal Beyond ($9.75), Slivers use Sliver Hive ($27), if most of your spells have more than one color in them then use Pillar of the Paruns ($12.50) and Unclaimed Territory ($2) works for any tribal deck since you name the creature type when you play it. Changeling decks will benefit from all these tribal lands. (except Corrupted Crossroads, and Pillar which care about other characteristics)
Path of Ancestry ($0.50) and Command Tower ($0.25) can both tap for any colour in your commander's identity, which means any colour in your deck and should be pretty much automatic included in any non-monocoloured EDH deck.

These costs can change wildly, Sliver Hive for instance was $7.50 when this post was first written, so check the costs for yourself for these cycles, the header for each section has been made into a link to the results for those cards on scryfall.