Using WolframAlpha with sympy to solve factorable quintics

Question

While trying to solve some factorable quintics with sympy, I noticed that it doesn't always find every solution, while wolframalpha does. Is there a way to use the softwares together, do something like:

if no sympy_solutions
    solve.with.wolfram(...)
end if

Here is an example of a factorable quintic that sympy doesn't know how to solve: 16*x**5 - 20*x**3 + 5*x - sqrt(5)/4 - 1/4.

Btw I have already tried the wolfram API, and it doesn't return exact roots, only approximations