CPU Spikes every 5 minutes with MySQL on RDS

Under a relatively write intensive load we are experiencing CPU spikes every 5 minutes using MySQL on RDS. Has anyone experienced something similar or have any idea what might be causing it?

MySQL Version: 5.6.22
Storage Engine: InnoDB

We experience the spikes on both M3 Medium and M3 Large instance types, with both magnetic and SSD disks, and they occur whether or not we have multi AZ enabled.

The more writes we have, the steeper the spikes are. However, the number of writes does not seem to impact the frequency. They continue a little while after we finish writing. They do not appear under a read only load.