1, 4, 9, 16
UPDATE
You missed one, you only wrote down 4, the first 5 are 1, 4, 9, 12, and 25.
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The first five perfect squares are: 1, 4, 9, 16, 25
There are infinitely many, just like in base 10. In any base system, the number of perfect squares is the same. Take the natural (counting) numbers 1, 2, 3, .... Squaring each of these produces the perfect squares. As there are an infinite number of natural numbers, there are an infinite number of perfect squares. The first 10 perfect squares in base 5 are: 15, 45, 145, 315, 1005, 1215, 1445, 2245, 3115, 4005, ...
12 + 22 + 32 + 42 + 52 = 1 + 4 + 9 + 16 + 25 = 55
Perfect squares cannot have digits after the decimal point.
There is no pair of perfect squares that sums to 21. And the question is pointless if it is not about perfect squares because in that case there are infinitely many answers.There is no pair of perfect squares that sums to 21. And the question is pointless if it is not about perfect squares because in that case there are infinitely many answers.There is no pair of perfect squares that sums to 21. And the question is pointless if it is not about perfect squares because in that case there are infinitely many answers.There is no pair of perfect squares that sums to 21. And the question is pointless if it is not about perfect squares because in that case there are infinitely many answers.