How fast should a competitive combo deck win?
Is a turn 5 win slow for Legacy?


Yes.

As of the current meta (from May 24th, 2018), Turbo/Dark Depths is the most represented Legacy combo deck, having around 6% of the field. This specific archetype can combo as fast as "Turn 0" with as few as 5 cards (a land that produces green mana, Crop Rotation, Vampire Hexmage and two Lotus Petal). It can consistently combo on turn 2 or 3, so this is usually what a combo deck should aim for.

The next 4 most represented decks are Storm, Show and Tell, Elves and Reanimator, all of which can consistently combo as soon as turn 2, but usually go off on turn 3-4.


When talking about Vintage, the most represented combo decks are PO Storm and Dredge. 
Vintage has a huge amount of 0 and 1 CMC mana accelerants, most of which are artifacts. Since the whole idea of the deck is to go off with Paradoxical Outcome, the PO Storm deck consistently goes off on turn 2, sometimes on turn 1.

Dredge decks don't benefit as much from the 0 and 1 CMC mana rocks, but it can usually go off on turn 2 or 3 with a couple of Bazaar of Baghdads.



The Modern metagame is all over the place, and it's mostly aggro decks, having 54% of the field. 

The most represented combo decks are Scapeshift, U/R Storm, GWx Devoted Company and Living End, all of which usually combo on turns 3-6, depending on mana acceleration and card draws.



The current Standard meta has no combo decks. The last time a combo decks had any relevant appearance in standard was during the BFZ-AKH standard, where both Aetherworks Marvel and Saheeli Cat decks worked more in a control role until they could go off. They're considered combo decks because their wincon is a combo, but they were not particularly fast.



Combo decks in duel commander (aka "The French list") are currently much underrepresented. The three most played decks still only represent about 3% of the field.

They're Iname, Death Aspect, which is a control/reanimator deck, and Prossh, Skyraider of Kher, which is a "cast my commander, hit you for 21" kind of deck. 

Teferi, Temporal Archmage is represented in both MTGO (9% of the field) and Duel commander (1%) and it is really a control deck that controls the game long enough to cast either Emrakul, the Aeons Torn (in MTGO) or Emrakul, the Promised End (in Duel).



Disclaimer: Every number mentioned in this answer was taken directly from MTGTop8, which really mostly takes MTGO into account when breaking down the metagame, so some of the numbers might be slightly off when talking about physical decks. Also, the information on how long a particular deck takes to combo comes from personal experience playing either with or against said decks and watching tournaments and streams.