last question team!

Given

  \(x+x^2+x^3+x^4=5\text{ ...(1)}\\\text{ add 1 to both sides}\\ 1+x+x^2+x^3+x^4=6\text{ ...(2)}\\ \text{ multiply both sides of (2) by x}\\ x+x^2+x^3+x^4+x^5=6x\text{ ...(3)}\\ \text{subtract (3) from (2)}\\1-x^5=6(1-x)\\ \text{Hence : }\frac{1-x^5}{1-x}=6\)

Here is my attempt I dont have time I have somwhat a hint
 

Undistribute x + x^2 + x^3 + x^4 = 5

x( 1 + x + x^2 + x^3) = 5

x( 1 + x( 1 + x + x^2) = 5

x( 1 + x( 1 + x(1 + x))) = 5

Now I will let anybody else work off from here.

I think you just keep on dividing by x and subtracting 1 from both sides.

Then simplify I am not sure.

Good luck everybody!

Thanks guys!