$\int_{0}^{5}(4 f(x)+g(x)) d x$

Step 1 ：The problem is asking for the integral of the function \((4f(x) + g(x))\) from 0 to 5.

Step 2 ：The integral of a sum of functions is the sum of the integrals of the functions. Therefore, we can separate the integral into two parts: \(\int_{0}^{5} 4f(x) dx\) and \(\int_{0}^{5} g(x) dx\).

Step 3 ：However, we don't have the specific forms of functions \(f(x)\) and \(g(x)\), so we can't calculate the exact values of these integrals. We can only express the answer in terms of these two unknown integrals.

Step 4 ：Final Answer: The integral of the function \((4f(x) + g(x))\) from 0 to 5 is \(\boxed{4\int_{0}^{5} f(x) dx + \int_{0}^{5} g(x) dx}\).