Question: Why the solve command doesn,t work for nonlinear system?

e1 := tau-gamma*S__1-beta*S__1*S__3/(S__3*alpha__1+1)-beta*xi*S__1*S__4/(S__4*alpha__1+1)+phi*S__5 = 0;
e2 := beta*S__1*S__3/(S__3*alpha__1+1)+beta*xi*S__1*S__4/(S__4*alpha__1+1)-(gamma+eta__1+eta__2)*S__2;
e3 := eta__1*S__2-(gamma+gamma__1+delta__1+omega)*S__3;
e4 := eta__2*S__2+omega*S__3-(gamma+gamma__2+delta__2)*S__4;
e5 := delta__1*S__3+delta__2*S__4-(gamma+phi)*S__5;
solve({e1, e2, e3, e4, e5}, {S__1, S__2, S__3, S__4, S__5});
 

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