I've been trying to recall a neighbour's experience with brain haemorhage. You had the haemorhage last month, say four weeks ago. You are (I presume) home and walking now.
Do you know why you had the bleed? That would make an enormous difference to the dangers of running - congenital weakness, or high blood pressure being, I would imagine, factors which would be likely to cause problems again, even if this bout is pretty well healed.
How much have you got back already? Are balance, muscle control, vision and all ok? I remember my neighbour being very tired and wanting to sleep all the time. She was in hospital for about 6 weeks. Presumably your being exhausted after 5 minutes is sort of like her sleeping all the time, possibly an indication of some degree of disruption still present.
I'm not a medic. I also believe in the value of a dream. Let us know.