Had just about a 7 hour layover in February but we were in T5 already - took Piccadilly line downstairs to Knightsbridge (about 45 minutes) had lunch and did some shopping at Harrods, came back and had ample time for a pre-flight meal in the lounge before boarding onward service. 6 hours including getting from T3 to T5 might be cutting it too fine.
Windsor is a good option - and yes, showers are available at Elemis Spa down at T5 South lounge area (between Concorde Room and Galleries lounge), functional and clean, not much more than that.