Vietnam is NOT a punter paradise and you may leave underwhelmed. To enjoy food you need to know how it works otherwise you are sitting in some tourist trap with english menu paying western prices eating shit food at 10x prices..
Vietnam is very safe for travelling and certainly safe solo. You will need Google translate in many places but in District 1 and mainstream tourist places english is fine. I encourage you to download and use Grab app. Use Grab bikes to get around.
You are only there for 5 days, not much time to make mistakes. If it was me, I would do day tours then go to Linh Cherry Little Tokyo once each day. Probably also fit in a 1-2 night tour to Mekong. While there are many places in Vn to see, Mekong is driving from HCMC so you aren't going through airports and losing time. Heaps of tourist places in D1 for booking tours.
I encourage you to hire local and private guides to maximise your experience.
For better punting advice check out the very active punter forum at
https://singlemanforum.com/vietnam/
I will leave you and your pre-travel research to solve your remaining question "Any difference HCMC and Saigon?"