You can find x intercept by using quadratic forumla if intercept actually happens.
x intercept occurs at y=0, so
x^2 +4x + 5 =0 ,
By finding discriminant using D = b^2 - 4ac we get:
D = 4^2 - 4*1*5 = 16 - 20 = - 4
Since the discriminant is less than 0, so the given equation does not have x-intercept.
Here is the graph of the equation that shows, it does not have any x-intercept.