This is a bit high level for you, isn't it? There is no way to solve a quintic equation in general, though there are some tricks you can employ. Graphically we can see how many real solutions there are. (There are three.)Solve for x∈ℤ.
x^5-15x^3-x-60 = 0
How do I get started? I think the solution is not over the real numbers.