However, OP, note that 4.5hrs is a bit tight to be able to pop into London - unless you know exactly where you're going and to pick up a specific item from a specific shop, for example.

You'll want to be back at T5 at least an hour before departure. The fastest route into town (assuming you want the Western side) is the Heathrow Express, for which you should probably factor in 35-45 minutes each way, including waiting time. So that's another 1.5 hours plus tube/bus/taxi from Paddington Station, or 2-2.5 hours if you're going to Central London by tube from T5. And if you went thro regular immigration as KARFA suggests (instead of going up to departures), it's probably going to be at least half an hour from aircraft to landside. So, unless you were going somewhere immediately adjacent to Paddington, you'd only have an hour or less in town, plus a lot of stress...

I wouldn't do it with a connection of less than 6 hours, I reckon, unless I was on my own and going to a specific shop.