Step 1: Write the balanced chemical reaction for the formation of water vapour: $\text{Hydrogen} + \text{Oxygen} \rightarrow \text{Water}$

Step 2: According to Gay Lussac’s Law and Avogadro's Law, two volumes of hydrogen combine with one volume of oxygen to give two volumes of water vapour. Thus, the volume ratio is $2:1:2$.

Step 3: The given volumes are 10 volumes of dihydrogen and 5 volumes of dioxygen. The ratio of given volumes is $10:5$, which simplifies to $2:1$.

Step 4: Since the given volumes are in the exact required ratio, 10 volumes of dihydrogen will completely react with 5 volumes of dioxygen to produce $10$ volumes of water vapour.