jmc

The first condition is equivalent to the statement that $a=4$ or $a=5$. The second condition is equivalent to the statement that $d=0$ or $d=5$. Finally, the third condition is equivalent to the statement that the ordered pair $(b,c)$ is one of the pairs $$(3,4),(3,5),(3,6),(4,5),(4,6),(5,6).$$In total, $2\cdot 2\cdot 6=\boxed{24}$ four-digit numbers $N$ satisfying the conditions.