Yes, you can still have an enjoyable safari in May despite it being a rainy season. The grass is fresh - so the herbivores are out in herds grazing while the carnivores are out to find prey as usual. The experience is just as magical.
Most of the major parks including: Maasai Mara, Amboseli, Samburu, Ol Pejeta, Lake Nakuru and Aberdare have well maintained roads and can be visited this time of year.
In the Maasai Mara, some low lying areas can experience flooding if the rivers burst their banks. This is however very rare and has little to no effect on game drives.
And on the plus side, the rates are much lower and there are far fewer crowds at this time of year.