Sure, I can help you create a test case generator for the given problem statement. Here's a Python function that generates random test cases based on the provided constraints:

```python
import random

def generate_test_case():
    # Step 1: Generate a random value for N within the constraints
    N = random.randint(1, 5000)
    
    # Step 2: Generate a random string s of length between 1 and N consisting of '0's and '1's
    length_of_s = random.randint(1, N)
    s = ''.join(random.choice(['0', '1']) for _ in range(length_of_s))
    
    return N, s

# Example usage:
if __name__ == "__main__":
    # Generate a test case
    N, s = generate_test_case()
    
    # Print the test case in the required format
    print(N)
    print(s)
```

This function `generate_test_case` will create random test cases that adhere to the problem's constraints. Here's a breakdown of the function:

1. **N Generation**: It generates a random integer `N` between 1 and 5000.
2. **String Generation**: It generates a random string `s` of a random length between 1 and `N`, consisting of characters '0' and '1'.

You can call this function multiple times to generate different test cases and print them in the required format for testing your solution.

Remember to use this generator responsibly, especially when generating large test cases, as it can produce a significant amount of data.