Complete the Two-Digit Prime Number: _5 Pattern Challenge

To solve this problem, we'll fill in the missing digit and verify the primality of the constructed number:

1. List potential digits to fill in the square: These range from 0 to 9.
2. Apply the prime number test for each potential number:
   • $05$: Not a valid number, as it's less than 10.
   • $15$: Divisible by 3 ($15 \div 3 = 5$).
   • $25$: Divisible by 5.
   • $35$: Divisible by 5.
   • $45$: Divisible by 5.
   • $55$: Divisible by 5.
   • $65$: Divisible by 5.
   • $75$: Divisible by 5.
   • $85$: Divisible by 5.
   • $95$: Divisible by 5.
3. After testing all candidate numbers, only $\mathbf{05}$ was incorrectly formed as it is less than 10. All other numbers are non-prime because they have additional factors; numbers ending with 5 are divisible by 5.
4. Thus, only $\boxed{05}$, where the $\square$ is replaced by $0$, fits the requirement, resulting in a more sensible reading as simply 5, which is indeed prime.

Therefore, the solution to the problem is $0$.