Early March is still a bit early for the rainy season so you might just get the odd thunderstorm. If birds are your real interest and you only have five days then probably the easiest is to go down to the Masai Mara via the Rift Valley lakes of Naivasha and Elementia or Nakuru. This would give you a good range of avian habitats and species in a short space of time. Don't forget as well that Nairobi itself has some excellent birding in the various forests and parklands in and around the city. Plus of course, there's the superb Nairobi National Park where you will see a lot of wildlife and birds.
