The product $55\cdot60\cdot65$ is written as a product of 5 distinct numbers.
Find the least possible value of the largest number, among these 5 numbers.
To solve the problem, we need to express the product \( 55 \cdot 60 \cdot 65 \) as a product of 5 distinct numbers and find the least possible value of the largest number among these 5 numbers.

1. **Calculate the product:**
   \[
   55 \cdot 60 \cdot 65 = (5 \cdot 11) \cdot (5 \cdot 12) \cdot (5 \cdot 13) = 5^3 \cdot 11 \cdot 12 \cdot 13
   \]
   \[
   5^3 = 125
   \]
   \[
   125 \cdot 11 \cdot 12 \cdot 13
   \]

2. **Factorize the product into 5 distinct numbers:**
   We need to find 5 distinct factors of \( 55 \cdot 60 \cdot 65 \) such that their product equals \( 55 \cdot 60 \cdot 65 \).

3. **Choose the factors:**
   Let's try to find a combination of 5 distinct factors. We can start by considering the prime factorization of the product:
   \[
   55 = 5 \cdot 11
   \]
   \[
   60 = 2^2 \cdot 3 \cdot 5
   \]
   \[
   65 = 5 \cdot 13
   \]
   Combining these, we get:
   \[
   55 \cdot 60 \cdot 65 = 5^3 \cdot 11 \cdot 12 \cdot 13
   \]

4. **Distribute the factors:**
   We need to distribute these factors into 5 distinct numbers. One possible way is:
   \[
   2, 3, 5, 11, 13, 12
   \]
   However, we need exactly 5 numbers. Let's try another combination:
   \[
   2, 3, 5, 11, 13, 12
   \]
   We can combine some of these factors to form distinct numbers:
   \[
   2, 3, 5, 11, 13, 12
   \]
   We can combine 2 and 3 to form 6:
   \[
   6, 5, 11, 13, 12
   \]

5. **Verify the product:**
   \[
   6 \cdot 5 \cdot 11 \cdot 13 \cdot 12 = 55 \cdot 60 \cdot 65
   \]
   \[
   6 \cdot 5 = 30
   \]
   \[
   30 \cdot 11 = 330
   \]
   \[
   330 \cdot 13 = 4290
   \]
   \[
   4290 \cdot 12 = 51480
   \]
   This matches the original product.

6. **Determine the largest number:**
   Among the numbers \( 6, 5, 11, 13, 12 \), the largest number is 13.

The final answer is \(\boxed{13}\)