Deeming a constant k such that the polynomial P(x,y,z)=x^5+y^5+z^5+k(x^3+y^3+z^3)(x^2+y^2+z^2) is divisible by x+y+z.

Determine a constant k such that the polynomial P(x,y,z)=x^5+y^5+z^5+k(x^3+y^3+z^3)(x^2+y^2+z^2) is divisible by x+y+z.