Answer
$x^{5}$
Work Step by Step
$(a+b)^{n}=\left(\begin{array}{l}
n\\
0
\end{array}\right)a^{n}+\left(\begin{array}{l}
n\\
1
\end{array}\right)a^{n-1}b+\left(\begin{array}{l}
n\\
2
\end{array}\right)a^{n-2}b^{2}+\cdots+\left(\begin{array}{l}
n\\
n
\end{array}\right)b^{n}$
-------------------
The coefficients are 1, 5, 10, 5, 1
$\left(\begin{array}{l}
5\\
0
\end{array}\right)=1=\left(\begin{array}{l}
5\\
5
\end{array}\right)$
$\left(\begin{array}{l}
5\\
1
\end{array}\right)=5=\left(\begin{array}{l}
5\\
4
\end{array}\right)$
$\displaystyle \left(\begin{array}{l}
5\\
2
\end{array}\right)=\frac{5\times 4}{1\times 2}=10=\left(\begin{array}{l}
5\\
2
\end{array}\right)$
The exponents of $(x-1)$ decrease from $5$ to zero
The exponents of $1$ increase from 0 to $5$.
Each term is $\quad \left(\begin{array}{l}
5\\
r
\end{array}\right)(x-1)^{r}\cdot 1^{n-r}$
problem expression = $[(x-1)+1]^{5}=x^{5}$
