The check is inside roots_quintic. Also, it's at the very top:
https://github.com/prasoon2211/sympy/blob/2fbfd20be96aa67d5bd18cf526e3ba9888f1ad85/sympy/polys/polyroots.py#L331

I think that this is more clearer. Since, we are checking for all sorts of things in the function, I think this is more straight forward for someone else reading the code than explicitly stating conditions for the coefficients to be integers outside the function.

Still, if it would be better to do the check outside, let me know and I'll implement it.