@Saddy-chin Alright, your specs look fine. Although I hope you've taken steps to cap your in-game frame rates? (If not, you should do that before anything else, although there's a chance it could help this problem as well.) And yes, just delete those five cache files, but not any others. You can delete everything in your FeaturedItems folder as well. And definitely make at least copy of your save so that you have a backup. You can do this in-game by using "save as" instead of saving and renaming it, or you can right-click on the save in your game folder and then copy and paste it somewhere else safe.
Also, at least for the time being, play offline (run Origin in offline mode, don't sign in at the launcher or Main Menu), disable the in-game shopping experience and the hidden object game loading screens... memories are a resource hog, but you probably have a lot of them. If you don't have the patience to clean them out on your existing sims, fine, but in the future you might want to consider turning them off.
So again, load up and try the travel transition. If it doesn't work, quit to desktop, reload, and try with just one sim. (You don't have to save this; just let me know if it works.) It would also be helpful if you tried a different travel destination, to find out whether it's the world you're sending your sims to or the travel mechanic itself that's causing all of these issues.
There are more things you can try, but let me know if any of this changes things. That will help determine what to do next. Oh, and if you've done anything to edit the destination world, that would be good to know as well.
Almost forgot, what world do your sims live in now? It might not matter, but it's worth checking out. And which other packs do you have in play. Each one adds to the game's overhead, lessening the resources left over to load both the home and destination worlds.