#### Answer

The $x$-intercept is: $2$.
The y-intercept is $5$.
See the graph below.

#### Work Step by Step

In order to find the $x$-intercept, we have to plug $y=0$ into the equation, and the $x$-coordinate will give us the intercept itself.
$5x+2y=10$
$5x+2(0)=10$
$5x=10$
$x=2$
The same thing should be done for the $y$-intercept, however, here $x=0$ should be plugged into the equation.
$5x+2y=10$
$5(0)+2y=10$
$2y=10$
$y=5$
The $x$-intercept is: $2$.
The y-intercept is $5$
Few other points that will help us plot the graph:
If $x=-4$
$5(-4)+2y=10$
$2y=30$
$y=15$
The point $(-4,15)$ is on the graph.
If $x=-2$
$5(-2)+2y=10$
$2y=20$
$y=10$
The point $(-2,10)$ is on the graph.
If $x=4$
$5(4)+2y=10$
$2y=-10$
$y=-5$
The point $(4,-5)$ is on the graph.