Yes so personally I think unless you have to (eg due to collecting a bag) you should get the airside bus from T3 to T5 rather than go landside. Once at T5 you can choose to go through arrivals and landside, or go to connections - personally I would go landside.

Usually the only circumstances I would head to connections would be when you are close to conformance as you will get to the bp check point for that a lot quicker than if you went landside.