First we get it in the form y= mx + b where m is the slope and b is the y-intercept
5x + 2y = 5 first subtract 5x from both sides
2y = 5 - 5x now divide both sides by 2
y = 5/2 - 5x/2 or y = -5x/2 + 5/2 where b= 5/2
The y-intercept is when x=0, thus plugging it into the y = -5x/2 + 5/2 gives us 5/2 thus the y-intercept is 5/2 or (0, 5/2)
The x-intercept is when y=0, now plugging it into 0 = -5/2x + 5/2 (subtract 5/2 to both sides) we get -5/2=-5/2x (divide both sides by -5/2) we get x = 1, this the x-intercept is 1 or (1,0)