Most big wildlife has left Tarangire National Park by this time so is not the best time to visit, but May is a great time to head to Moru Kopjes in the Serengeti as many wildebeest are passing through before heading north.
Towards the end of the month as the rains start to pass you may be fortunate enough to have numerous dry days. A positive factor of travelling at this time is that there is notably less dust around due to the ground still remaining damp, and also significantly fewer tourists. As the climate changes over the years no one can guarantee when the rains will stop so this could be a great time to get cheap prices yet fair weather for your safari.