The slope intercept form of an equation is y=mx+b
In this form b is the x intercept and m is the slope
for your equation you have y=5x+1
so you know the slope is 5/1
and the y intercept is 1
to get the x intercept you can set y to 0 and solve for x
0=5x+1
subtract 1 from both sides
-1=5x
divide by 5
x=-1/5
that is your x intercept.