I'm with Frank on this one.
Since dragons normally increase by hit die, you'll need to compare the power of the dragon after advancing it to CR 21 via hit dice versus adding 5 levels of Psy Warrior.
I'm almost positive you will find a Wyrm Black Dragon (CR 20) will be able to mop the floor with an Old Black Dragon Psy Warrior 5.
One of the biggiest areas that the dragons will be disparate in is spellcasting ability. The Old Dragon will have a caster level of 7th and Manifestor level of 5. The Wyrm will have a caster level of 13.
Also, the Wyrm dragon will have a higher armor class, more hit dice, a better BAB, better saves, and better ability scores (even if you use the elite array for the Old Dragon)
I'd probably treat the class levels in Psy warrior as nonassociated, since they do not keep pace with the dragon's natural BAB (not even by half) nor do they augment it's natural spellcasting ability