If you want exact answers try Maxima, I did and found that it didn't
even know how to do the exact 3 and 4th order answers..
Maxima actually knows closed solutions to third and fourth order polynomials
(I have 5.9.3):
string(solve(a*x^4+b*x^3+c*x^2+d*x+e,x));
(%o13) [x = -sqrt(-((18*a^2*(sqrt(-256*a^3*e^3-(-192*a^2*b*d-128*a^2*c^2+144*a\
*b^2*c-27*b^4)*e^2-((144*a^2*c-6*a*b^2)*d^2+(18*b^3*c-80*a*b*c^2)*d+16*a*c^4-4\
*b^2*c^3)*e+27*a^2*d^4-(18*a*b*c-4*b^3)*d^3-(b^2*c^2-4*a*c^3)*d^2)/(6*sqrt(3)*\
...... many more lines for this expression ....