In which pair of substances do the nitrogen atoms have the same oxidation state?

$ \textbf{(A)}\ \ce{HNO3} \text{ and } \ce{ N2O5} \qquad\textbf{(B)}\ \ce{NO} \text{ and } \ce{HNO2} \qquad$

${\textbf{(C)}\ \ce{N2} \text{ and } \ce{N2O} \qquad\textbf{(D)}}\ \ce{HNO2} \text{ and } \ce{HNO3} \qquad $
To determine the oxidation state of nitrogen in each compound, we will use the following rules:
1. The oxidation state of hydrogen (\(\ce{H}\)) is usually \(+1\).
2. The oxidation state of oxygen (\(\ce{O}\)) is usually \(-2\).
3. The sum of the oxidation states of all atoms in a neutral molecule must be zero.

Let's calculate the oxidation state of nitrogen in each compound:

1. **\(\ce{HNO3}\):**
   - Let the oxidation state of nitrogen be \(x\).
   - The oxidation state of hydrogen is \(+1\).
   - The oxidation state of each oxygen atom is \(-2\), and there are three oxygen atoms.
   - The sum of the oxidation states must be zero:
     \[
     +1 + x + 3(-2) = 0
     \]
     \[
     1 + x - 6 = 0
     \]
     \[
     x - 5 = 0
     \]
     \[
     x = +5
     \]

2. **\(\ce{N2O5}\):**
   - Let the oxidation state of nitrogen be \(x\).
   - The oxidation state of each oxygen atom is \(-2\), and there are five oxygen atoms.
   - The sum of the oxidation states must be zero:
     \[
     2x + 5(-2) = 0
     \]
     \[
     2x - 10 = 0
     \]
     \[
     2x = 10
     \]
     \[
     x = +5
     \]

3. **\(\ce{NO}\):**
   - Let the oxidation state of nitrogen be \(x\).
   - The oxidation state of oxygen is \(-2\).
   - The sum of the oxidation states must be zero:
     \[
     x + (-2) = 0
     \]
     \[
     x - 2 = 0
     \]
     \[
     x = +2
     \]

4. **\(\ce{HNO2}\):**
   - Let the oxidation state of nitrogen be \(x\).
   - The oxidation state of hydrogen is \(+1\).
   - The oxidation state of each oxygen atom is \(-2\), and there are two oxygen atoms.
   - The sum of the oxidation states must be zero:
     \[
     +1 + x + 2(-2) = 0
     \]
     \[
     1 + x - 4 = 0
     \]
     \[
     x - 3 = 0
     \]
     \[
     x = +3
     \]

5. **\(\ce{N2}\):**
   - Nitrogen in its elemental form has an oxidation state of \(0\).

6. **\(\ce{N2O}\):**
   - Let the oxidation state of nitrogen be \(x\).
   - The oxidation state of oxygen is \(-2\).
   - The sum of the oxidation states must be zero:
     \[
     2x + (-2) = 0
     \]
     \[
     2x - 2 = 0
     \]
     \[
     2x = 2
     \]
     \[
     x = +1
     \]

From the calculations, we see that the nitrogen atoms in \(\ce{HNO3}\) and \(\ce{N2O5}\) both have an oxidation state of \(+5\).

The final answer is \(\boxed{\textbf{(A)}}\)