If $f(x)$ is a polynomial with integer coefficients, and $a_{1}, a_{2}, a_{3}, a_{4}, a_{5}$ are distinct integers such that $f(a_{1}) = f(a_{2}) = f(a_{3}) = f(a_{4}) = f(a_{5}) = 2015$, then find the number of integral solutions of the equation $f(x) = 2016$.