SN74LS93N is not counting as expected
I see two issues:


No decoupling caps. Edit: Add decoupling caps (see comment). When ICs switch state they draw a pulse of current on the 5V. Your power wires have enough inductance to cause the 5V to momentarily dip to near zero. This causes the IC to lose it memory.
No series resistors on your LEDs, although some LEDs have built-in resistors, so I can't be sure.


For more information, you need to draw a schematic, I can't see all the connections.