5 pounds at 34+ weeks really isn't that big. Babies don't put on much weight after 37, so even if you're baby gained another pound a week you'd only have an 8 1/2 pound baby. Not tiny but could be much larger. I personally would never ask for a c-section, I don't want major surgery that takes longer to heal from. Yes natural labor is tough, but I went through 15 hours no meds ended up with 2 stitches and stopped bleeding after 10 days. It was nothing really!
My doc or any doctor where I live will not do csection unless needed that is a major surgery and insurance may not pay for voluntary section. Believe me recovery is a lot easier for natural and with me this pregnancy is a lot worse after my csection
At this stage your baby can be going through a growth spurt and measuring ahead, my son measured very big around 35 weeks and he was only 8lbs 9.5ozs, it's very possible to have your baby naturally even if she's big, my friend is only 5' and she had a 10lb baby. It depends on your doctor if he/she will let you have a voluntary c-section but there's a lot more complications with a c-section than natural delivery, and your next delivery (if you chose to have more children) will automatically be another c-section unless you find a doctor willing to do a VBAC. Talk to your doctor about your concerns and see what he/she can do for you, good luck!!