Dilutions do not work that way. You must take into account that by adding 40 mL of dilute water, you are changing the final volumes and concentrations. The proper way to calculate this:
(200 mL)(5 dkH) = (x dkH)(240 mL)
Solving for x = 4.167 dkH.
It's been 30 years since I did Chemistry. A lot has vaporised.