I'm 5 days post op, how long will I be unable to breathe through my nose after Rhinoplasty?

There is both external and internal swelling following rhinoplasty. Additionally, sometimes during surgery, internal nasal splints or packing is placed and once this is removed, nasal airflow improves significantly. Resolution of internal swelling and hypersensitivity will depend largely on what was done during rhinoplasty surgery both externally and internally - concomitant septal or turbinate  or sinus surgery. If there was significant nasal airway obstruction prior to surgery and this was addressed, most patients notice a significant improvement immediately after surgery. In other cases, patients may have a lot of internal swelling and hypersensitivity, this typically improves a few weeks after surgery but can take up to 3 or 4 months to improve significantly. During this recovery period, saline nasal spray, or steroid nasal spray may be necessary to obtain temporary relief from symptoms until full recovery has occurred. You should discuss your concerns with your surgeon during your follow-up visits.

Have patience!  You are only 5 days post op, so swelling is expected for both the internal and external nose.  It takes weeks to months for all the swelling to settle, but you should be breathing a lot better within days.  Follow up with your Plastic Surgeon for an exam as he recommends, so that he can monitor your healing.  Best wishes!