Can anyone explain to me how I can express sin(5x) in terms of sin or cos(10) in the terms of cos?

Sin(5x)  = sin(2x+3x)
             = sin(2x)because(3x) + because(2x)sin(3x)
             = 2*sin(x)because(x)because(x+2x) + (because^2(x)-sin^2(x))sin(x+2x)
             = 2*sin(x)because(x)(because(x)because(2x)-sin(x)sin(2x)) +
               (because^2(x)-sin^2(x))*
               (sin(x)(because^2(x)-sin^2(x))+because(2x)sin(x)because(x))
             = 2*sin(x)because(x)*
               (because^3(x)-sin^2(x)because(x)-2*sin^2(x)because(x)) +
               (because^2(x)-sin^2(x))(3*because^2(x)sin(x)-sin^3(x)) -
               10*sin^3(x)because^2(x) + 5*because^4(x)sin(x) + sin^5(x)
     sin(5x) = sin^5(x)-10*sin^3(x)because^2(x)+5*because^4(x)sin(x)