You might have a five hour lay over, but if you have to claim luggage and change terminals you may need to knock time off. Also, you might have to check in again, which means you may have to turn up an hour before the flight, so you might actually find yourself with only three hours to spare.
I take the Piccadilly line every week. It sucks. On Friday it took an hour to get from Hatton Cross to Hammersmith. I don't think I'd risk going all the way to South Ken unless you have a clear 5 hours at least.
Vicky