It will certainly be wet. Take a brolly!
We went to the South Coast one year in May for three weeks. It rained every day. Often for just 40 minutes and then the sun would shine through. I seem to remember that it only rained for one complete day (unlike Weston Super Mare in the ‘50s) during the whole three week period. The day it rained we rented hotel bikes and cycled to Ukunde, at least we were wet and warm.
On one safari we had unexpected rain at the Masai Mara (not in May) and it was still very good, it didn’t stop our enjoyment. The only annoying thing for me was the windows kept steaming up. To see a large pride of lions soaked to the skin approx 10 metres from the safari vehicle is something to treasure. The safari drivers have to deal with the rain all the time and it only takes them a couple of minutes to place or remove the roof shutters. I would suggest that if you do book a safari during the short or long rainy seasons you make sure that your vehicle has 4 wheel drive otherwise your driver will be restricted on the routes he can take you.
You should still enjoy your holiday despite the rain.