He has gone to hospital five times. This means it is possible for him to go one more time
He went to hospital five times. That Means it is not possible for him to go one more time for the same reason, he maybe got better,or maybe he died
No, these sentences aren't talking about possibility. They essentially say the same thing the only difference is simple past verses present perfect.
MRF, you're right. The choice of "has gone" versus "went" depends
entirely on whether the speaker thinks that the action may occur again.
I think that Jim misinterpreted your post.
The use of the two sentences depends on both the viewpoint of the speaker and the situation. The first one is used to express that there have been five visits within a period of time, and the person it refers to may still have the illness which made him spend time at the hospital, therefore the string of events may have a continuation. The second one, on the other hand, implies that the time span we refer to ended sometime in the past, and at the moment a sixth visit is not likely to happen, because the reason for going to the hospital is no longer there. So I also think MRF is right, I just would not speak of possibility in this context, but likelihood.