Answer
\begin{align*}
\text{$x$-intercept: }&
\left(-\dfrac{5}{7}, 0\right)
\\
\text{$y$-intercept: }&
(0, 5)
\end{align*}
Work Step by Step
To find the $x$-intercept of the given equation, $
y=7x+5
,$ substitute $y=0$ and then solve for $x.$ That is,
\begin{align*}
0&=7x+5
\\
-7x&=5
\\\\
\dfrac{-7x}{-7}&=\dfrac{5}{-7}
\\\\
x&=-\dfrac{5}{7}
\end{align*}
To find the $y$-intercept of the given equation, substitute $x=0$ and then solve for $y.$ That is,
\begin{align*}
y&=7(0)+5
\\
y&=0+5
\\
y&=5
\end{align*}
Hence, the intercepts of the given equation are
\begin{align*}
\text{$x$-intercept: }&
\left(-\dfrac{5}{7}, 0\right)
\\
\text{$y$-intercept: }&
(0, 5)
\end{align*}
