OMM 1997 Problem 6

Prove that number $1$ has infinitely many representations of the form $$1 =\frac{1}{5}+\frac{1}{a_1}+\frac{1}{a_2}+ ...+\frac{1}{a_n}$$ , where $n$ and $a_i$ are positive integers with $5 < a_1 < a_2 < ... < a_n$ .