All real numbers except -4 and 9.
The domain of an expression is the range of all values for which the expression is defined. Looking at the expression, it will legal everywhere except when a^2 - 5a - 36 is equal to 0. Since that's a quadratic equation, we can use the quadratic formula to find where its value is 0, giving -4 and 9.
Therefore the domain of the expression is, All real numbers except -4 and 9.