#### Answer

$$y=(x-2)^{2}+1$$

#### Work Step by Step

Given $$y=x^{2}-4 x+5$$
\begin{align}
y&=x^{2}-4 x+5\\
&=\left(x^{2}-4 x+4\right)+1\\
&=(x-2)^{2}+1
\end{align}
begin with the graph of $y=x^{2}$ in Fig.(1), shift $ 2$ units to the right in Fig.(2), and then shift upward $1$ unit in Fig(3).