What is the value of the discriminant, b2 − 4ac, for the quadratic equation 0 = x2 − 4x + 5, and what does it mean about the number of real solutions the equation has?

In your problem a = 1, b = -4 and c = 5
so discriminant is -4
the discriminat is the value under the radical so if the number is negative there is no real solution.
if the number is 0 there is one solution
if the number is positive there are two solutions

The first answer is correct