Limits of Products and Quotients

Given 3 functions $f(x) = \cos(x)$, $g(x) = \sin(5x) + 3$, and a continuous function $h(x)$ defined on all real numbers. If it is known that $f(x) \cdot h(x) - g(x)$ approaches $0$ when $x$ approaches $0$, then what is the value of $h(0)$?