As Andy stated, you must use two of the same model of controller to establish a cluster.
5.8.4 is the last version released by Zebra before the WiNG portfolio was sold to Extreme, and that version appears to have AP621 support, and it is within the supported versions of the NX5500, so it is within the realm of possibility to replace the controllers first and then roll out newer APs without incurring significant down time, and then upgrade to the latest firmware release.