My house is in desperate need of a good cleaning. Its one or the other
should I clean or exercise?

Put on some music and clean with gusto! It's exercise, really!

I say workout for 10 mins to get your heart rate up and THEN clean with gusto -

Yeah - or jog in place during cleaning tasks. I have done this before. Stretch extra high to windex those mirrors. When putting things away, take one item to the appropriate room at a time...for example, jog one book back to your bedroom, then come back and jog another.