$\begin{array} { l }\lim_{y \rightarrow 5} \left(y-\frac{ 25 }{ y }\right),\\\lim_{y \rightarrow 5} \left(y-5\right)\end{array}$
Evaluate the limit$\begin{array} { l }0,\\\lim_{y \rightarrow 5} \left(y-5\right)\end{array}$
Evaluate the limit$\begin{array} { l }0,\\0\end{array}$
Since the expression $\frac{ 0 }{ 0 }$ is an indeterminate form, try transforming the expression$\lim_{y \rightarrow 5} \left(\frac{ y-\frac{ 25 }{ y } }{ y-5 }\right)$
Write all numerators above the common denominator$\lim_{y \rightarrow 5} \left(\frac{ \frac{ {y}^{2}-25 }{ y } }{ y-5 }\right)$
Simplify the complex fraction$\lim_{y \rightarrow 5} \left(\frac{ {y}^{2}-25 }{ y \times \left( y-5 \right) }\right)$
Use ${a}^{2}-{b}^{2}=\left( a-b \right)\left( a+b \right)$ to factor the expression$\lim_{y \rightarrow 5} \left(\frac{ \left( y-5 \right) \times \left( y+5 \right) }{ y \times \left( y-5 \right) }\right)$
Cancel out the common factor $y-5$$\lim_{y \rightarrow 5} \left(\frac{ y+5 }{ y }\right)$
Evaluate the limit$\frac{ 5+5 }{ 5 }$
Simplify the expression$2$