677, because the square of the first number plus one equals the second number, and the square of the second number plus one equals the third number; The square of the third number plus one equals the fourth number, and so on. The square of the fourth number plus one equals the fifth number. Namely:

The square of 1+ 1 = 2,2+1= 5,5+1= 26,26+1=677, so the number after 26 is 677.