Welcome back!
The mechanical differences will be readily apparent. Fixed target numbers, damage codes and armor work differently, Limits, the Matrix, etc.
There are also major stylistics differences, like the fact that the differences between hermetics and shaman have narrowed, and that the wireless Matrix lets the deckers and riggers run around with the rest of the group so that their work is more integrated with the rest of the team rather than being mini-games that no one else participates in, etc.
But for all that, the biggest differences might be in terms of flavor. I don't necessarily have the language to accurately describe the changes, but the short version is that the 2070s are different from the 2060s which were different from the 2050s.
Medcineman, one of the oldest of the old-timers around here (member #80 out of ~7,500) once described SR1/2 as cyberpunk, SR3 as dystopian, and SR4/5 as transhuman. Others were making the distinction between cyberpunk and post-cyberpunk. I don't know all the ins and outs of these terms but I think you'll pick up on what he meant as you update yourself on the current setting.
Life in the Sixth World is still hard, death is still easy, but to me the world is less bleak than it was in SR1-3. Back then, the world was new and weird and the developers were still figuring out what to do with it while making things up on the fly. Now that the game is approaching 30 years old, and many of the developers grew up playing it, so things are more established and the world is more settled than it used to be.
I have a pet theory that the tone of the game changed when they went from printing the books in black-and-white on uncoated paper (SR1-3) to printing them in color on glossy paper stock (SR4-5). For me, the greyscale artwork really lent itself to a grim cyberpunk setting, as did the monochrome nature of the books themselves. Then SR4A had the blue background on every page while SR5 has the tan-and-red background to the core rulebook, and the pages are all shiny. Now, the artwork and books are so bright and colorful and reflective that sometimes it feels harder to find the shadows. But that's just a personal opinion and I haven't found anyone else who shares it yet.
Again, welcome back. Your situation is not unique so feel free to reach out to the community as questions arise.