5 minutes is probbly way to short. Clients will be attempting to re-ip roughly every 2.5 minutes, so having the lease that short is increasing the amount of DHCP traffic happening in the background.
The DHCP discover message is a broadcast, so how it progates will depend on how/if you have broadcast filtering enabled on the VAP. DHCP renewals (which should be the majority of your traffic, unless guest connections are typically < 2 minutes in duration), will be unicast to the original DHCP assigning server, and revert back to broadcast if renewal fails.
That said, if you're cycling out IP allocations every 5 minutes and still running out of IPs, then you're on the right track to increase the number of available IPs either through increasing the scope from /22 to /21, or by splitting the sites across different /21s.