Problem:
Find the largest number which divides 70 and 125 leaving remainders 5 and 8 respectively.

Solution:

To find the largest number that divides two given numbers leaving specific remainders, we need to use the concept of the highest common factor (HCF) or greatest common divisor (GCD).

Step 1: Finding the factors of the given numbers

To find the largest number that divides 70 and 125, we need to first find the factors of these numbers.

Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70
Factors of 125: 1, 5, 25, 125

Step 2: Identifying the common factors

Next, we need to identify the common factors of 70 and 125.

Common factors: 1, 5

Step 3: Checking the remainders

Since the question states that the number should leave a remainder of 5 when divided by 70 and a remainder of 8 when divided by 125, we need to check if the common factors satisfy these conditions.

Checking the remainder when divided by 70:

1 % 70 = 1 (remainder is not 5)
5 % 70 = 5 (remainder is 5)

Checking the remainder when divided by 125:

1 % 125 = 1 (remainder is not 8)
5 % 125 = 5 (remainder is not 8)

Step 4: Finding the largest number

From the above calculations, we can see that the common factor 5 satisfies the condition of leaving a remainder of 5 when divided by 70. However, it does not satisfy the condition of leaving a remainder of 8 when divided by 125.

Therefore, the largest number that divides 70 and 125 leaving remainders 5 and 8 respectively is not 5.

Final Answer:
The correct answer is option 'A' (13).