The domain is (probably) the whole of #RR#, the set of all real numbers since the function #h(x)# is well defined for all values of #x in RR#. The reason I say #RR# rather than #CC#, #NN#, #ZZ# or #QQ# is based on the notational convention that #x# normally stands for a real number.
If the domain is #RR#, then the range is #{y in RR: y >= -5}#.