The Fibonacci sequence modulo 5 is defined by $a_n \equiv a_{n-1} + a_{n-2} \pmod{5}$ with $a_0 = 1, a_1 = 1$. Compute the sequence until it repeats the pair $(a_i, a_{i+1}) = (1, 1)$. What is the period (Pisano period modulo 5)?