Answer
x-intercept = 2
y-intercept = 5
Refer to the image below for the graph.
Work Step by Step
Write the equation in $Ax +By=C$ form.
This will make solving for the intercepts a lot easier.
The given equation can be rewritten as:
$5x+2y-10=0
\\5x+2y-10+10=0+10
\\5x+2y=10$
To find the $x$ intercept, set $y=0$ then solve for $x$ to obtain:
$5x+2y=10
\\5x+2(0) = 10
\\5x=10
\\\dfrac{5x}{5}=\dfrac{10}{5}
\\x=2$
The x-intercept is $2$.
To find the $y$ intercept, set $x=0$ then solve for $y$ to obtain:
$5x+2y=10
\\5(0)+2y = 10
\\2y=10
\\\dfrac{2y}{2}=\dfrac{10}{2}
\\y=5$
The y-intercept is $5$.
To draw the graph of the equation, plot the x-intercept point $(2, 0)$ and the y-intercept point $(0, 5)$ and connect them using a straight line.
(refer to the attached image in the answer part above)