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

**Step 1:** Identify the degrees of the numerator and denominator. The numerator is \( x^2 - 7 \) which is of degree 2. The denominator is \( 5x^5 + 3 \) which is of degree 5. **Step 2:** Compare the degrees. Since the degree of the numerator (2) is less than the degree of the denominator (5), the horizontal asymptote is determined by the fact that the function approaches zero as \( x \) approaches infinity or negative infinity. **Step 3:** State the horizontal asymptote. The horizontal asymptote of the function is \[ y = 0. \]