Determine the horizontal asymptote of the graph of the following function. \( h(x)=\frac{x^{2}-7}{5 x^{5}+3} \)

When determining the horizontal asymptote of the function \( h(x)=\frac{x^{2}-7}{5 x^{5}+3} \), we look at the degrees of the polynomial in the numerator and the denominator. The degree of the numerator, which is \(2\), is less than the degree of the denominator, which is \(5\). In such cases, the horizontal asymptote is at \(y=0\), indicating that as \(x\) approaches infinity or negative infinity, the value of the function approaches zero. So, the horizontal asymptote of \( h(x) \) is \( y = 0 \).