There are infinitely many combinations beyond 3, 4, 5
Three natural numbers (a, b, c) that satisfy a²+b²=c² are called a Pythagorean triple. Besides famous examples like 3-4-5 and 5-12-13, there are actually infinitely many such combinations. There is a formula that generates a triple from just two numbers, m and n.
Euclid's formula: Choose natural numbers m and n with m > n > 0. Then a = m²−n², b = 2mn, and c = m²+n² always satisfy a²+b²=c². Moreover, if m and n are relatively prime and one is even while the other is odd, the triple becomes a primitive Pythagorean triple that cannot be reduced any further.