5 hour and 20 minute Saturday layover at London Heathrow

First of all, it's not really a "layover", it is connection time. You arrive at 9:20 am, if your flight is on time. Big, big IF. Then you have to disembark (20 minutes?) and get in the very, very long queue for Passport Control. (Unless you have an EU passport for which the lines are shorter for flights arriving from N. America.) By the time you get through that the better part of an hour will have passed, so let's say it is now 10:30 am. For your flight at 2:40 pm you'll need to go through security and that takes forever at Heathrow so you should start that process by about 12:40 pm and the walk to your gate could take as long as 20 minutes. There are signs indicating how long it takes to walk to Gate so-and-so from "You are Here".

There is not time to leave the airport. Relax. Have lunch. Buy something in the Duty Free. Bon voyage.

They frequently offer tastings in the "World of Whisky".

It is the old 5 hour window. Look like a lot but isn't when you do the math. Just enjoy the airport -- maybe sleep a little.

Heathrow is notoriously slow for flight transfers. But at least with all the shops and pubs, it's not a bad place to be stuck for a few hours.

I assume you'll be arriving from an overnight flight and will still have a long day ahead. Look into getting a day pass for one of the airlines lounges. AA is $50 + VAT for their arrivals lounge(per person). British Air has some real nice lounges in T5, but I don't think they sell day passes (too bad b/c they have free liqour). Not sure about any other airlines though. Anyway, it's more relaxing that terminal seating and you would have a chance to freshen up.

1) Is your connecting within the UK or out of it...that will have a lot to do with timing

2) What terminal are you arriving in, and which one are you leaving from?