I'm not entirely sure what you did there here's what would be a good idea:
∫ dv/dt dt = k∫1/t^2 dt
v= -k/2t^2 + d
now you know that when t=1 v=3, and you also know that the limiting velocity (when t→∞) is 5, so when t→∞, d=v, and v= 5, so d = 5, so now you have the formula
v=-k/2t^2...