14-2 and 14-3 into one box
No.  You've created a wiring loop.  

There's a fundamental rule that currents must be equal in each cable or conduit.   The way you accomplish that is by laying your cables in a tree topology. Any number of branches, but branches can't ever rejoin each other.   

You need to air-gap either the two things in box 5, or air-gap the two switches in box 1. 

Stick a partition inside the box and no wires cross it. Partitions are mandatory for separating low-voltage wiring from mains wiring in the same junction box.   Truth be told they're not physically mandatory in this case, but the idea of total separation is mandatory.  

In fact, I really do recommend physical separation because if you don't, it's a matter of time before some gooberhead decides he wants to put a smart switch in a 3-way remote location, so he crosses the partition to poach a neutral wire.  And now you have an illegal loop. 

Also remember you can take power to the lamps first and double-back to the switches in a "switch loop", but if you do, Code requires you to use 14/3 in the switch loop. That will leave a spare wire, which is future neutral for use by smart switches.