1. Check each statement for group 15 elements

Group 15 elements are: $\mathrm{N, P, As, Sb, Bi}$.

Their common properties include oxidation states $-3, +3,$ and $+5$, and down the group the inert pair effect becomes more significant.

2. Statement (A): Dinitrogen is a diatomic gas which acts like an inert gas at room temperature.

• $\mathrm{N_2}$ is indeed a diatomic gas.
• It is very unreactive at room temperature because of the strong triple bond, $\mathrm{N\equiv N}$.
• So it behaves almost inert at room temperature.

Hence, (A) is correct.

3. Statement (B): The common oxidation states of these elements are $-3,+3$ and $+5$.

• This is a standard property of group 15 elements.
• Nitrogen commonly shows $-3, +3, +5$.
• Heavier members also commonly show $+3$ and $+5$.

Hence, (B) is correct.

4. Statement (C): Nitrogen has unique ability to form $\mathrm{p}\pi-\mathrm{p}\pi$ multiple bonds.

• Nitrogen, due to small size and high electronegativity, forms strong multiple bonds like: $\mathrm{N\equiv N},\quad \mathrm{C\equiv N},\quad \mathrm{N=O}$
• This is indeed a characteristic feature of nitrogen.

Hence, (C) is correct.

5. Statement (D): The stability of $+5$ oxidation states increases down the group.

• Due to inert pair effect, the stability of the lower oxidation state $+3$ increases down the group.
• Therefore, the stability of the higher oxidation state $+5$ decreases down the group.

So (D) is incorrect.

6. Statement (E): Nitrogen shows a maximum covalency of 6.

• Nitrogen is a second-period element.
• It has no vacant $d$-orbitals and cannot expand its octet.
• Therefore, its maximum covalency is 4, not 6.

So (E) is incorrect.

7. Incorrect statements

The incorrect statements are: $\boxed{(D) \text{ and } (E)}$

This corresponds to Option B.

8. Comparison with stored correct answer

Stored correct answer: B

Our derived answer: B

So the answer matches the stored correct answer.