Is it normal to have swelling in the cheeks and bruising 5 weeks post lower transconjunctival bleph? (photo)

This is especially true after a fat repositioning.  It is also very common if a patient has had more bleeding than normal during a surgery.  I would recommend some warm towels to help speed up the healing.       

The bruising does bring its own swelling.   Overall you look to have a very nice early result.  I don't think you should be concerned about this.  Some surgeons might offer laser of fotofacial to help speed up the resolution of the last bit of bruising.  However, even without this treatment this bruise will clear.  While my crystal ball does not tell me when this will clear, it is likely to be in the next couple of weeks.  As it goes, the swelling will also resolve.

Swelling after lower eyelids

In patients undergoing a simple transconjunctival blepharoplasty, one
should expect only minimal if any swelling after 5 weeks. Ask your doctor if
you has a more advanced procedure, like fat transposition. In this case, you
still could have some residual postoperative swelling. Your doctor should be
willing to see you at any time to answer your questions and concerns