5276 = 2 x 2 x 1319.
5276 is the number of binary strings of length 14 with no substrings equal to 0000 or 0010 (A164387).
5276 is a number n such that n - 3, n + 3, and n + 5 are all primes (A144842).
5276 is the number of moves needed to solve the 4-peg Tower of Hanoi puzzle with 22 disks (A160002).
5276 cannot be written as a sum of three squares.