5 weeks post op, will the tip of the nose improve and not look so over-projected? (Photo)

It is common to still have swelling at this stage after surgery that can alter the appearance of the nose, especially the tip as this area tends to stay swollen longer than others.  Give it some time as it can take 6-12 months for final results to be apparent. 

It is too early to come to a conclusion about the final results. The tip in the rhinoplasty is the slowest part to finally heal. The swelling in the tip takes one full year.

It's still really early in your recovery so the final result is hard to determine. 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. If you are concerned I would recommend following up with your surgeon. 

It is still too early to determine what the final result of your rhinoplasty will be.  The majority of swelling after rhinoplasty resolves by about 4 weeks, but there is still some swelling even up to 6-12 months. Also, it is not unusual to have asymmetric swelling or prolonged tip swelling. I recommend following up closely with your surgeon and expressing your concerns to him or him. Best of luck.