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.