On the solution of the equation $\frac5k=\frac1x+\frac1y+\frac1z$ on the set of natural numbers $N\setminus \{60 n + 1, n\in N\}$

In the present paper it is shown that for every number $k\not\equiv1$ (mod 60) the equation $\frac5k=\frac1x+\frac1y+\frac1z$ has at least one solution $(x, y, z)\in N$.