Yeah, I know where this is going. ;-)

The biggest flaw:

Your battery is 5Ah. If it is a typical battery, it is good for 5amp draw (i.e. 1 C). The smallest controllers are 15amps. So you will try to draw 3 times the power it is capable of delivering. So, you will have serious voltage sag, and kill the battery in no time.

good idea though.

Plan B: Get three of these, wire them in parallel for 40v15ah, and you might have a shot.