Is there any way to solve for "r" or is the best way by using trial and error?

I don't know how to solve this to get a closed-form solution. However, you can simplify a bit, and then use an approximation technique to get a very close answer. So if you substitute x = 1+r, and divide the equation through by 2, you get:

25 = x + x^2 + x^3 + x^4

Using a technique such as Newton's method (nicely explained by galactus here: https://www.askmehelpdesk.com/mathematics/quadratic-solve-e-x-e-x-2-2-sinhx-2-a-470457.html ) you find that there are two answers: x=1.890629 and x = -2.45276. So r = 0.890629 or r = -3.45276

Thank you for your help!