For what values of (m) does the graph of y=mx²-5x-2 have no x-intercepts?

You need to find where the discriminant is less than zero
Remember the discriminant is b^2 - 4ac
a = m
b = -5
c = -2
Set up the inequality like this
(-5)^2 - 4m(-2) < 0
25 + 8m < 0
8m < -25
m < -25/8 < -3.125

So any number less than -3.125 will make this graph have no x-intercepts (or real roots)