I never get it when people say playing one game will take away from another. I've never had that problem. Final Fantasy V is Final Fantasy V and Final Fantasy III is Final Fantasy III, they're two different games with two different systems and casts of characters.

I played III after V and I enjoyed it all the same.
They have similar systems (specifically class-related) despite Final Fantasy III "originating" the idea. Final Fantasy V provided significant improvements and is, overall, a better game for it.