I almost have the answer but I can't quite get there.

Differential equation is

dH/dt= (40-H)^2/100

I solved it through here:

H= 40 - 200/(2t + 5)

However, when I plug in a value t=5 I get the wrong answer. My professor has this but the following step says:

H=80t/(2t+5)

How do I get to that?