cyclic5 381 Bytes
cyclic5:=[x1+x2+x3+x4+x5, x1*x2+x2*x3+x3*x4+x4*x5+x5*x1,x1*x2*x3+x2*x3*x4+x3*x4*x5+x4*x5*x1+x5*x1*x2,x1*x2*x3*x4+x2*x3*x4*x5+x3*x4*x5*x1+x4*x5*x1*x2+x5*x1*x2*x3,x1*x2*x3*x4*x5-1];
time(gb:=gbasis(cyclic5,indets(cyclic5),with_cocoa=false));
gb;
//time(gb:=gbasis(cyclic5,indets(cyclic5),tdeg,with_cocoa=false));
//gb;
time(gb:=gbasis(cyclic5,indets(cyclic5),with_cocoa=true));
gb;