5khz? That's .2 ms for a single cycle of your signal. 3200 processor cycles, divided by how fine you want to slice up the full cycle. And you want to do sine's and cosines and floating point multiplications on this? Might be possible if you sample the AKD every now and then and precalculate the sines and cosines.
But remember, the output will be a pulse-width modulated square wave, not a sine wave, and will have an accuracy of 8 bits.