Worst-case trials to match five keys to five locks

Five distinct keys each open exactly one of five distinct locks, with a one-to-one correspondence. Using the best possible procedure, what is the largest number of key-in-lock attempts you might need before you know which key belongs to every lock?

$10$. For the first lock, at most four keys need testing, since if four fail the fifth is known. Then three for the next, then two, then one: $4+3+2+1=10$.