How to solve non linear and transcendental equations with five roots

How to solve non linear and transcendental equations with five roots FIve equations are there;

    cos(x1)+cos(x2)+cos(x3)+cos(x4)+cos(x5)=0.9;;
    cos(5(x1))+cos(5(x2))+cos(5(x3))+cos(5(x4))+cos(5(x5))=0;;
    cos(7(x1)))+cos(7(x2))+cos(7(x3))+cos(7(x4))+cos(7(x5))=0;;
    cos(11(x1))+cos(11(x2))+cos(11(x3))+cos(11(x4))+cos(11(x5))=0;;
    cos(13(x1))+cos(13(x2))+cos(13(x3))+cos(13(x4))+cos(13(x5))=0;;

0<x1<x2<x3<x4<x5<90degree;;

where x1,x2,x3,x4,x5 are angles in degree.. How to solve it with Generic Algorithm/PSO/Newton-Raphson or any kind of optimization technique? How to write these functions in matlab coding?

[Walter Roberson]

I am not convinced there is a solution.