Funny - I just came back from a trip that hit all of those countries!
I would suggest either Japan, with visits to several cities, or splitting your time between Hong Kong and Singapore.
I love Vietnam, and have spent a lot of time there (as I have in Japan and HK) but I agree it would be more difficult with a 5 year old. Saigon in particular can be very challenging, even for adults - it is hot, noisy, dirty, crowded, and has worse traffic than I have ever seen in my life. And that’s coming from someone who loves it there! There is no public transportation to speak of (Uber worked great, though!) and crossing the street is worse than an advanced level of a game of Frogger. Plus the food could be a big challenge for a kid, much as I love it, unless you’re keeping yourself insulted, which defeats the purpose. I don’t think kids need to be totally insulated or coddled, I just think the level of discomfort one has to accept in order to have an authentic experience there is higher than in a lot of other places.
Singapore is very easy, though also hot, and the food is great. It’s less…interesting and exciting, shall we say, and has a lot in common with a big shopping mall, but I think the intersection of ease and authenticity here would be a better choice with a kid in tow. Hong Kong can be a bit grittier, but if you’ve never done a big Asian city, it’s pretty exciting, and I think would be for a child as well. There are plenty of direct flights, and if you’re flying Cathay, the airport experience - checking your luggage in from either Kowloon or HK Station up to 24 hours in advance!! - is very smooth. Subways in both HK and Singapore are great as well.
Japan has its own challenges, depending on what you want to experience there. but it is very easy as a tourist to design a wonderful trip, almost no matter what you like to do. Travel within Japan, either by train or plane, is super easy and it’s no problem to get a few different places in within an 8 day journey. In the bigger cities, it’s also very easy to get around, and the tourist destinations are actually pretty special.
Let us know what you decide. You’ll have a great trip no matter what.