Answer
$x^5+5x^4z+10x^3z^2+10x^2z^3+5xz^4+z^5$
Work Step by Step
Using the coefficients in the $r=5$ row of the Pascal's triangle, $\left\{
1,5,10,10,5,1
\right\}$, and the pattern in expanding binomials, then $
(x+z)^5
$, expands to
\begin{array}{l}
x^5+5x^4z+10x^3z^2+10x^2z^3+5xz^4+z^5
.\end{array}
