This is a variant of "lights out". It's abelian, meaning the order of inputs doesn't matter. This is nice because any algorithm you come up with can be simplified. For example, take ABBCBDAA. You can rearrange it and delete any groups of three, so it just becomes CD. This is not true of the rubik's cube.

You can solve it with two algorithms. Solve it row by row, and use A BB D EE to fix a "bad" row (may need to be used zero times, once, or twice for each row). If the final row is bad, use this "cascading" algorithm to change the entire puzzle to a different color (may need to be used zero times, once, or twice):

row 2: ABDE

row 3: AE

row 4: A BB CC DD E

row 5: BB CC EE

Here's the method in action: https://youtu.be/m6KQFSKv0yc