Recovery speed depends a lot on your general health and fitness, in my case I was out of the hospital in 5 days and back to work in 3 weeks. The main source of pain of course is your broken sternum, when you cough, sneeze, laugh, but amazingly it starts healing fairly quickly, they will give you a pillow that you embrace everytime you need to sneeze, etc so that it dampens the effect of the strain on your chest, you will also get pain medication. I can tell you, they discovered my aneurysm after an MTB accident, I broke my leg and needed surgery, my open heart surgery was 3 months after my leg surgery (I did not want to wait so I had it as soon as feasible) the pain from my broken leg far exceeded the pain from the open heart surgery.
I know open heart surgery sounds scary, but it is nothing compared to a disecting aneurysm, think about it this way, you know you have it and can do something about it, you are one of the lucky ones, a lot of people don't get that chance. In my case, I'm not going to lie I was nervous before surgery, but the stress of knowing I had a ticking bomb in my heart far exceeded the stress of surgery, I wanted it done as soon as possible.
As others said, find a thoracic surgeon that is an expert on aneurysms, someone who does this often, and get the support of a good cardiologist, also someone who specializes on aneurysms, if possible it is better if they belong to the same team and communicate, it makes a world of difference. Talk to them about any fear you have, the recovery, the details of the surgery, anything that gives you doubt or fear, they will have the answers.
I hope everything goes well, and yes ask me any questions you want to ask me, that is what this forum is for, to give each other advice and support.

I had this surgery in an emergency situation because I had a complete sudden aortic dissection in 2015. You don't want that kind of emergency. I had no idea I had an issue until my aorta burst on a business trip 1500 miles from home and then it was a nightmare scenario. Do not wait. You can get all your work, estate, insurance, house, and family issues in order and let everybody know that you need their support. It's open heart surgery and it's a huge deal. BUT BUT BUT, you will be fine. This is a great opportunity to get to a great surgical center that is totally prepared for your case with all of the blood, materials, staff, and surgeons in place and scheduled. You are going to be fine, but listen to your doctors. If you are at a 5.2cm you need to have the surgery done. Everybody's recovery is different, but I'd say you will be moving pretty well after 2 months and feeling back to your old self within a year. It really depends upon your age, your physical health, etc. They will manage your pain, but nothing is free. I have had 9+ years of a great life after it happened to me at 50 years old. You're going to be fine but get it done. Make sure your surgeon is at least 50+ years old. She/he will have done thousands of operations. University of Minnesota, Mayo, Cleveland Clinic, UCSD-San Diego (where I had mine done) are all fantastic. The trick is to be brave and get it done. You owe it to yourself and your family. Peace.