Find the average value of the function $f(x)=x^{2}-7$ on $[0,6]$.

Step 1 ：The problem is asking for the average value of the function \(f(x)=x^{2}-7\) on the interval \([0,6]\).

Step 2 ：The formula for the average value of a function \(f(x)\) on the interval \([a, b]\) is \(\frac{1}{b-a}\int_{a}^{b}f(x)dx\).

Step 3 ：In this case, \(f(x) = x^{2}-7\), \(a = 0\), and \(b = 6\). So, we need to calculate the integral of \(f(x)\) from \(0\) to \(6\), and then divide the result by \(6-0=6\).

Step 4 ：The calculation gives us an average value of 5.

Step 5 ：Final Answer: The average value of the function \(f(x)=x^{2}-7\) on \([0,6]\) is \(\boxed{5}\).