Like you, I have an Anthem A5 amp that I was using both for 2 channel music and for 5.1 movies. Like you, I was satisfied with the A5 for movies, but not for music. I elected to go the route suggested already by several posters, namely, I kept the A5 and used it to amplify the center channel and the rears, and I added a stereo amp for the FR and FL channels. Hence there are two channels on the A5 that go unused.
The stereo amp I added was the Pass XA30.5, and I am very happy with the results. Compared to the A5 in 2 channel listening conditions, the XA30.5 is more transparent, detailed, and harmonically correct.
As for the concern, raised by some posters, that you want matching amplification across the front three channels, I am of the opinion that, while that is ideal, it is by no means necessary for a satisfying 5.1 experience. The reason, I believe, has a lot to do with how most movies are mixed, in that dialogue is nearly always placed in the center channel only, while music and effects are placed disproportionately in the FL and FR channels. So most 5.1 mixes are already "unmatched," as it were. When you add to that the fact that, when watching movies, your attention is split between listening to the audio and watching the images, any differences in amplification matching are likely to be below the threshold of awareness, IME.
Of course, YMMV. Good luck.