If the three real zeros of a function f(x) are located at x = r, x = q, and x = p, determine (if possible) the?

Let g(x) = f(x-5). At x=5+r, we have g(x) = g(5+r) = f(5+r - 5) = f(r) = 0, so 5+r is a root. That should be more than enough of a hint, if I've interpreted your question correctly.