Among all the numbers representable as $36^k - 5^l$ ($k$ and $l$ are natural numbers) find the smallest. 
Prove that it is really the smallest.
1. **Understanding the problem**: We need to find the smallest positive value of the expression \(36^k - 5^\ell\) where \(k\) and \(\ell\) are natural numbers. 

2. **Analyzing modulo 10**: 
   - For any natural number \(k\), \(36^k \equiv 6^k \equiv 6 \pmod{10}\).
   - For any natural number \(\ell\), \(5^\ell \equiv 5 \pmod{10}\).
   - Therefore, \(36^k - 5^\ell \equiv 6 - 5 \equiv 1 \pmod{10}\).

3. **Form of the expression**: From the above, we conclude that \(36^k - 5^\ell\) must be of the form \(10n + 1\) for some integer \(n\).

4. **Finding the smallest positive value**:
   - For the smallest positive value, we start with \(n = 0\). This gives us the equation \(36^k - 5^\ell = 1\).
   - Rearranging, we get \(36^k - 1 = 5^\ell\).
   - Using the difference of squares, we can write \(36^k - 1 = (6^k + 1)(6^k - 1) = 5^\ell\).

5. **Analyzing the factors**:
   - Let \(6^k + 1 = 5^a\) and \(6^k - 1 = 5^b\) where \(a\) and \(b\) are natural numbers such that \(a > b\) and \(a + b = \ell\).
   - Subtracting these two equations, we get \(5^a - 5^b = 2\).

6. **Contradiction**:
   - The equation \(5^a - 5^b = 2\) has no solutions in natural numbers because the left-hand side is always a multiple of 5, while the right-hand side is 2, which is not a multiple of 5.
   - Therefore, there are no solutions for \(n = 0\).

7. **Next smallest value**:
   - We try \(n = 1\). This gives us the equation \(36^k - 5^\ell = 11\).
   - Testing small values, we find that \(k = 1\) and \(\ell = 2\) satisfy the equation: \(36^1 - 5^2 = 36 - 25 = 11\).

8. **Verification**:
   - We need to verify that there are no smaller positive values. 
   - Since \(36^k - 5^\ell \equiv 1 \pmod{10}\), the next possible value would be \(21\), \(31\), etc., but these do not satisfy the form \(36^k - 5^\ell\) for small values of \(k\) and \(\ell\).

Thus, the smallest positive value of \(36^k - 5^\ell\) is indeed \(11\).

The final answer is \(\boxed{11}\).