It entirely depends on what you're looking for. If you like history, art, architecture and shopping, coffee and Italian food, then absolutely, definitely Buenos Aires. It is a huge city and each neighbourhood has a different vibe, so I'd recommend spending time in some different ones if you can. (The safest for a tourist are in the centro/downtown, Palermo, San Telmo, Recoleta, I visited them and loved them all.) 5 days is a good amount of time to see the city, though you might not feel it's enough.
I am also originally from the midwest and very familiar with Chicago and felt Buenos Aires was no better or worse, safety-wise, than Chicago. I've felt shockingly unsafe the last few times I've been in downtown Chicago, so you might feel more at ease in some parts of BA (like I did). The only tip I'd have is do not flash your camera (or smartphone if you have one) more than you have to. I felt more comfortable with a small, non-fancy point-and-shoot digital camera since it doesn't attract much attention. If you are a woman, avoid carrying a large purse and take one that goes across your body, not just over your shoulder - I say this mainly because that's what the local women seemed to carry and I followed suit. Other than all you need to do is be aware of your surroundings and don't stray out of the "safer" neighbourhoods (much like Chicago). I felt safer there than I do in some American cities.
Everyone says Santiago is safe, but a friend recently spent some time there with a group of people who let their guard down and were mugged. So, don't let your guard down, just like you shouldn't in downtown Chicago or anywhere else.
I don't seem to suffer from jet lag as much when travelling to South America as I do when travelling to Europe.
Have fun making plans!