The colored frame is implying something, but the colors of Flame-Spray Dragon & Grave-Breaker Dragon don't matter, you are paying with color-agnostic creatures.

I could see this work better is there a (high) mana cost e. g. , but each dragon part reduced the cost by e. g. (or you could make the cost reduction a part of the dragon part parameter e. g. red creatures with dragon pars actually reducing red mana costs).

This would have the added effect that the cards don't become dead if you don't have five specific dragon parts worth of creatures available to cast them.

Does this have haste and enter with a haste counter? Weird - especially since haste is an ability that makes less sense on a counter.

Other cards care about colors, so for simplicity's sake I was going to give many of the elder dragons colors.

Yeah, these dragons would be dead in hand and might be better invoked the sideboard. That could probably be done.

The idea of the haste and caring about the haste counter is that if you really needed this dragon, and a dragonpart gave Flame-Spray Dragon haste, there would be some extra bonus.