Groebner bases – system of polynomial equations with known root

I have 5 polynomial equations for 5 variables, and I know that the set of roots is finite. All coefficients are integers. Eventually, I'd like to find all the roots, but finding the Groebner base is impossible (I've tried maple, Mathematica, or Sympy), probably because it takes too much or too much memory. But I found a fairly simple root by looking only at the equations. Now, I want to use the fact that 1 root is known to reduce the set of polynomials to lower order if possible to simplify the problem. How would I tackle that?