If you have been working as software engineer for five years, but can't solve that task, that indeed makes me doubt how were you hired in the first place. I'm sorry if that sounds harsh; I appreciate your honesty and I would want to support you in your self-doubt, but I consider honesty to be more valuable in such a situation than being nice.
Caesar's algorithm in particular looks like a high school assignment, to be honest.
To be honest, I'm only just able to write a program in C, which is the required language for these CS50 tasks.
I've never been asked to do this kind of work before, so I had no idea where to really start.
The walkthroughs provided in the course gave me a high level overview to the solution required, but being able to translate that pseudo-code, if you will, was the part which I was completely stuck on for a while.
I felt like I should have known at least how to start off solving this problem using prior knowledge I had gained through commercial experience, but I was wrong, and none of my experience thus far was able to guide me in the direction which ended up with an answer to the problem.
A thing that may help: Approach this CS50 material as if you have no knowledge of programming. Set aside your preconceptions about both your ability and the nature of programming itself (to the extent that this is possible). Review the materials and read/watch all of it, even the things that you know. You may know them, but exercise the discipline to persist through them and practice the material.
I've since learned to also follow along using the walkthroughs provided, since they provide answers to the most basic of questions that I would have asked.
I would suggest you have a golden opportunity here, tbh. You have identified an area of useful skills which you currently are lacking - and a source of info where to learn. That's good. More importantly than that, your fianceè is currently doing the course and is right at the start! If you sign up to CS50 now (it's free!), you have maybe 4-6 hours of lectures to catch up before you are at Ceasar yourself, and then you can work through this excellent course together!
You will learn lots, some of which may be very useful. As will your fianceè. And you'll both have a much easier and fun time having a partner to discuss the lectures and problem sets, helping each other out here and there, before having to reach out for assistance.