Locks and keys so any three of five can open

Five people share a safe. They want any group of $3$ or more of them to be able to open it, but no group of $2$ or fewer. The safe gets several locks, all of which must be opened; each lock may have several copies of its key, but a key fits only its own lock. What is the minimum number of locks, and how many keys does each person carry?

$10$ locks; $6$ keys each. Every pair must be shut out by some lock whose keys they both lack, and that lock's keys must be held by all three others; distinct pairs need distinct locks, giving $\binom52=10$ locks with $3$ keys each. The $30$ keys spread evenly, $6$ per person.