Once the cast is off, is it likely to drop down and be a normal nose?

Yes once the cast comes off the nose will drop and look more normal, the swelling will also start to go away at that time. 

 It truly takes 1 full year for the entire dorsum (profile) and sidewalls of the nose to fully heal and for all the swelling to dissipate. Rhinoplasty healing is a tedious process because it is one of the only surgeries where we are not removing excess skin. It takes 3 years for the tip to fully heal (only if significant tip work is performed). The tip takes the longest time to heal and mold to the new framework because it is the thickest skin of the nose. The skin over the profile is thinner than the skin over the tip. Patience is required during this healing phase. Great idea to talk to your surgeon about your concerns but keep in mind healing takes time.

I am glad that you are addressing your concerns with your Surgeon, which is ultimately the best way to handle these situations.  However, you can expect your nasal tip position to migrate downward over time.  One of the most common concerns patients have immediately post-operatively is elevated tip position. This is usually by design, expecting later downward rotation.  Remember that it takes a year for swelling to resolve after rhinoplasty. 

Thank you for your question. 
With any nasal surgery, the name of the game is patience. At one week, we would expect you to have quite a bit of swelling and bruising still noticeable and may have trouble breathing out of one or both nostrils. By the end of two weeks, typically, you will still be swollen but look more like you have a bad cold, rather than post surgical. Swelling can take up to a year to be completely gone, however, by 9 weeks you will look very good and should see big difference from your pre-op pics.

At 5 days out, it is too early to tell what your nose will look like. You are tapped and splinted. Please be patient.

Typically, the initial swelling after nose surgery subsides within two to three weeks. However, residual swelling, especially in the tip of the nose, can take about a year to resolve as the contour refines. Swelling can also vary through the day, being more prominent in the morning. It's always best to follow up with your surgeon regarding concerns/questions since they know exactly what was done during surgery. Try and be patient as your nose continues to heal.