Upvote:4
If your travel agent has booked these as a single trip (ie checking your luggage straight through), putting a similar connection plan into the Heathrow connection planner indicates that you can actually travel between terminals on a dedicated connections shuttle bus (note: the train journey does not actually take 20 minutes, but it isn't that frequent so travel time PLUS wait time can be up to 20 minutes). Once you get to terminal 3 you will reclear security.
The minimum connection time listed for T5 to T3 is 90 minutes, so you may not have time to dawdle but it's a valid connection so if indeed you have a through ticket the airline has to assist you if there are delays.