hypo residual chlorine testing using a 10ml reagent pack
This is sort of an extended comment, not necessarily an answer.

Overall, yes I'd expect different numbers at least. How they would vary is a matter of some conjecture. 

(1) The Hach DR 900 is a colorimeter. I'm not sure how large of a sample you need to fill active volume of the colorimeter cell.

(2) The ratio of water volume relative to the amount of solid reagent is changing. So the chemical equilibrium on which the calibration curve depends might shift. If you dilute 5 and 10 ml samples to 15 ml with "pure" water and take 10 ml of each of the three samples (2 dilutions plus "full strength"), then you be comparing better.

(3) Even given (2), the results seems odd. Normal drinking water should have between 0.2 and 2.0 mg/L. 


Is pH of the water ok? 
Does water have some unusual buffer capacity? 
Reagent pack old? 
Do you have some standards which you can test?