>189,195
　題意より s=x+y+z=0, t=xy+yz+zx=-10, u=xyz=4√3.
　x^2=X, y^2=Y, z^2=Z とおくと、
　S = X+Y+Z = s^2 -2t =20, T = XY+YZ+ZX = t^2 -2su =100, U = XYZ = u^2 =48.
(与式) = X^5 +Y^5 +Z^5 = S^5 -5TS^3 +5ST^2 +5US^2 -5UT = 272000.

注) X^n +Y^n +Z^n ≡σ(n) とおくと、σ(0)=3, σ(1)=S, σ(2)=S^2 -2T,
　σ(n)=S･σ(n-1)-T･σ(n-2)+U･σ(n-3).