Can you have 2 circuits in one box?
Yes, you can -- just mind the box fill and labeling, and make sure to keep your neutrals separated!
A five gang box composed from gangable, 2¾&quot; deep boxes as you describe provides 70in³ of fill (14in³/gang as per the Steel City catalog).    You are bringing 4 14/3, 3 14/2, and 2 12/2 cables into the box, in addition to mounting five devices in it, three of which are connected to 14AWG wire and the other two connected to 12AWG wire.
This means that we are using 72¾in³ of fill; 36in³ for the 18 14AWG wires, 9in³ for the 4 12AWG wires, another 9in³ for the two receptacles, 12in³ for the lighting controls, and finally 6¾in³ for equipment grounding, as per the 2020 NEC rule that requires an extra equipment grounding allowance for every four additional ground wires past the initial allowance's worth.  This is just a hair over what your box supplies, and would be legal under the 2017 NEC fill rules as the fill for the additional grounding wires is what pushes it over the top, but doesn't account for any cableclamps internal to the box. As a result, I would go with a 3½&quot; deep box if you are sticking with the field-gangable boxes, or order in a factory-fabricated 5 gang box that is taller and thus provides more fill volume if you'd rather go that route.
You'll also want a consistent way of labeling your wires so that you can tell the various circuits involved here apart; crossing your streams could lead to false AFCI trips, overloaded neutrals, and other such badness.  Thankfully, premade wire labeling booklets are available for this job, and make this relatively simple; all you have to do is come up with a consistent scheme for using them.
Finally, even if you don't use the wire labels, you must keep your neutrals on the two circuits separate for the reasons mentioned above. However, you also must join all the equipment grounding wires involved together and pigtail them off to the box and to the receptacles (unless they are self-grounding that is).  (Think of how this'd turn out if you were wiring this in Chicago, where you'd have to use metal conduit instead of cables.)  In fact, you could use a divider in your box between the three lighting controls and the two receptacle devices; you'd then need grounding pigtails in both compartments, but it would make it much easier to keep your circuits apart.