near zero i think. it is the checked bags which will sink him.

best case he is stepping off at 1920. he has immigration (shouldn't be too bad at that time) and a wait for bags, optimistically 10-15 mins. so we are already at say 1940 by now. tube or HEX/crossrail to T5. HEX/crossrail station is closer to T3 with trains at 1930, 1942, 1957, 2000 so if he can get the one at 1942 that should be ok, otherwise he should head for the tube.

bag drop closes 45 minutes before, and he needs to be going through security no later than 35 minutes before.

so i would say it is possible, but every single thing needs go in the right direction for him to just make it. one thing goes wrong, for example a 20 minute wait for bags, and it is game over.