Yes, I just did this on Saturday (between Terminal 5 and Terminal 1). You will have to go through Customs and Inspection, which should not take a long time once you make the lengthy walk off the airplane to that area. Filling out the landing card(s) on the plane and NOT when you get to the Inspection area to save additional time. Then you may have another check-in and passport/boarding pass inspection at your airline, depending on your carrier. Our lay-over was 90 minutes, and we were 25 minutes late arriving. We made it to the next flight just as they were boarding it, after really speeding through all the walking as fast as we could. So gauge your time accordingly! There are lots of signs telling you exactly which way to go. We didn't have to get on a bus or anything, it was a (relatively) direct walk. By the way, if you have a connecting flight, why exactly do you need to carry your luggage? They should book it on through. If you have to collect your luggage, add at least 30 minutes to your connection time. MAKE SURE that you have your connecting flight's boarding cards issued when you get on the first flight so that you save yourself a LOT of time with the connection. Best of luck!

There are both buses and trains between the Terminal 1/2/3 area (they are close together) and Terminal 5. The train is probably easiest and runs every 15 minutes from Heathrow Central to the basment of T5. http://www.heathrowairport.com/portal/page/Heathrow%5EGeneral%5EAirport+information%5ETravel+between+terminals