If you have the Symbolic Math Toolbox, this will give you one set of solutions:
syms a b c d e
Eqns = [32.5 == 2*sqrt((a*b-e^2)/(a*((1/c)+2/(sqrt(a*b)+e))));
81 == 2*sqrt(sqrt((a^2-d^2)/(b*((2/(a-d))+(2/(a+d)))))*(sqrt((a*b-e^2)/(a*((1/c)+2/(sqrt(a*b)+e))))));
230 == b-(2*e^2/(a+d));
0.3 == (b*d-e^2)/(b*a-e^2);
0.3 == e/(a+d)];
[as,bs,cs,ds,es] = vpasolve(Eqns, [a,b,c,d,e])
All the solutions are complex, so they may have complex-conjugate solutions as well. I will leave you to explore those.
