There is no general analytical solution for quintic algebraic equations, but a Newton-Raphson numerical method can be used:
So s ≈ -1.253462
There are four other solutions as well, but these are all complex.
Here's the graph.......https://www.desmos.com/calculator/t1f4fhif21
[Desmos shows the root to be -1.25......Alan's answer is closer to the truth....!!! ]
Thanks Chris. I should have mentioned that it's always a good idea to draw a graph for these sort of problems, if only to get a good initial estimate to start off a more accurate numerical iteration method.