jmc

Since $17=\frac{51}{3}<\frac{52}{3}<\frac{54}{3}=18$, the floor of $52/3$ is $17$. The given quantity is thus equal to $$\lceil \frac{17}{5/23}\rceil =\lceil \frac{391}{5}\rceil =\lceil 78.2\rceil =\boxed{79}.$$