Can -4 over -5 be written as 4 over 5 (for a y=mx +c gradient question?

m = (-4)/(-5)
= 4/5

(-4) / (-5) =4/5

the negatives cancel out

I'm not sure what you're really trying to say, sorry!

If you meant the y-intercept is -4 and x-intercept is -5, the formula for the gradient should be

m = - ( y-intercept / x-intercept )
= - (-4/-5)
= - 4/5

Yes.

(-4)/(-5) = 4/5

First, I'm not sure why this is a question that needs to be asked anonymously. It's not controversial or personal. Are you being hunted by the FBI? :)

Answer:
Yes, the negative signs cancel out
m = (-4)/(-5) = 4/5

Yes, in the context of the slope of a line, (-4)/(-5) is equal to, and can be replaced by (4)/(5). However, you are correct to be concerned about making that substitution, because there is one instance, at least, in which making that substitution can leave you facing the wrong direction.

Take the case where the sine of an angle is sinΘ = -a, and the cosine is cosΘ = -b. The tangent of the angle is sinΘ/cosΘ = (-a)/(-b) = tanΘ. The angle whose tangent is (-a)/(-b) is in Quadrant III while the angle whose tangent is (a)/(b) is in Quadrant I. In this particular case, (-a)/(-b) and (a)/(b) are not interchangeable.