The number N when divided by 16 gives the remainder 5__________________ is the remainder when the same number is divided by 8.

Answer

To solve the problem step by step, we can use the information given about the number \( N \) and apply Euclid's division lemma.

### Step-by-Step Solution:

1. **Understanding the Problem**: We know that when the number \( N \) is divided by 16, it leaves a remainder of 5. This can be expressed using Euclid's division lemma:
\[ N = 16q + 5 \]
where \( q \) is the quotient when \( N \) is divided by 16.

2. **Finding the Value of \( N \)**: From the equation above, we can express \( N \) in terms of \( q \):
\[ N = 16q + 5 \]
Here, \( q \) can be any integer (0, 1, 2, ...).

3. **Dividing \( N \) by 8**: Now we need to find the remainder when \( N \) is divided by 8. We can substitute the expression of \( N \) into the division by 8:
\[ N = 16q + 5 \]

4. **Calculating \( N \mod 8 \)**: We can simplify \( N \) modulo 8:
\[ N \mod 8 = (16q + 5) \mod 8 \]
Since \( 16 \mod 8 = 0 \), we have:
\[ N \mod 8 = (0 + 5) \mod 8 = 5 \]

5. **Conclusion**: Therefore, the remainder when \( N \) is divided by 8 is:
\[ \text{Remainder} = 5 \]

### Final Answer:
The remainder when the number \( N \) is divided by 8 is **5**.