Find the area of the region bounded by the graphs of the given equations. \[ y=x^{2}+5, y=x^{2}, x=0, x=3 \]

Step 1 ：We are given the equations \(y=x^{2}+5\), \(y=x^{2}\), \(x=0\), and \(x=3\). We are asked to find the area of the region bounded by these graphs.

Step 2 ：The area between two curves is given by the integral of the absolute difference of the two functions over the given interval. In this case, the two functions are \(y = x^2 + 5\) and \(y = x^2\), and the interval is from \(x = 0\) to \(x = 3\).

Step 3 ：We can find the area by integrating the absolute difference of these two functions over this interval.

Step 4 ：The absolute difference between the two functions is \(|x^2 + 5 - x^2| = 5\).

Step 5 ：The integral of 5 from 0 to 3 is \(5 * (3 - 0) = 15\).

Step 6 ：Final Answer: The area of the region bounded by the graphs of the given equations is \(\boxed{15}\).