Find the area under the curve $y=8 x^{4}$ over the interval $[0,5]$ Give the exact value.

Step 1 ：The area under a curve y=f(x) from x=a to x=b is given by the definite integral of f(x) from a to b. In this case, we need to find the definite integral of \(8x^{4}\) from 0 to 5.

Step 2 ：Let's denote x as x and f as \(8x^{4}\).

Step 3 ：By calculating the definite integral, we find that the area under the curve is 5000.

Step 4 ：\(\boxed{5000}\) is the exact value of the area under the curve \(y=8 x^{4}\) over the interval [0,5].