Are all UTXOs locked by an address spent in a transaction? Imagine I have 2 UTXOs locked by my address, each of which allows me to spend 5 bitcoins.

If I subsequently want to send just 2 bitcoins to someone else, will both UTXOs be used as inputs in the transaction, where I now receive 8 BTC change as a single UTXO locked to my address, or as the value I want to spend can be covered by a single UTXO, is only one of the 5 BTC UTXOs spent by the transaction and I receive change in a new UTXO worth 3 BTC locked by my address. So now my address locks two UTXOs, one for 5 BTC which was not needed in this transaction, plus the change I just received for 3 BTC. Or something else?
Transactions explicitly refer to which UTXOs they are spending.

You can construct a transaction which only spends one of the two 5-BTC UTXOs, and sends 2 BTC to the destination and 3 BTC to a (possibly new) address of yourself.

You can also construct a transaction which spends both, and sends 8 BTC back to yourself. Or it could have multiple outputs that send funds back to yourself, summing up to 8 BTC.

In short: there is nothing special about the two UTXOs that share an address, apart from the fact that the same key can sign for both - but it doesn't have to.