625. A typesetter spilled part of the set - a five-digit number that is a perfect square, written with the digits $1,2,5,5$ and 6. Find all such five-digit numbers.
$\triangle$ Among the given digits, a perfect square can end in 1, 5, or 6. Let's consider all three cases.

1) Suppose the square ends in 1.

Since the second-to-last digit of a perfect square in this case must be even (see the statement of problem 566 from § 13), it is either 2 or 6. Let's form all possible five-digit numbers:

$$
\text { 65521, 56521, 55621, 25561, 52561, } 55261 .
$$

Numerical verification shows that none of them is a perfect square.

2) Suppose the last digit of the square is 5.

Then the second-to-last digit is 2 (see the statement of problem 563 from § 13). We get the numbers

$$
15625,16525,61625,56125,61525,65125 .
$$

Among them, only the first one is a perfect square: $15625=125^{2}$.

3) Suppose the last digit of the desired number is 6.

Then the number is divisible not only by 2 but also by 4. Consequently, based on the divisibility rule for 4, its second-to-last digit is 1 or 5. Let's form all corresponding numbers:

$25516,52516,55216,12556,15256,21556,25156,51256,52156$.

None of them is a perfect square.

Answer: $15625=125^{2}$.