python lists, appending something to the list changes the entire thing?

I don't see the actual sort that you're doing, but in general:

Lists are mutable. Any change you make to it affects all links to that list. To make a copy of it and break its connection to other references, you need to return alist[:]

def s_sort(numbers):
  alist=[]
  #do actual sorting here and swap numbers/index if neccessary

       alist.append(numbers)
  return alist[:]  # this makes it a copy!

def main():
    numbers=[5,7,3]
    print(s_sort(numbers))
main()

Your code doesn't actually do what you say it does. In fact, it doesn't even run. But here's a simple example that does demonstrate the problem you're seeing:

def s_sort(numbers):
    alist=[]
    alist.append(numbers)
    numbers.sort()
    alist.append(numbers)
    return alist

The problem is that alist is not a list of two different lists, it's a list of the same list twice in a row. So, when you modify that one list, of course that one list is modified everywhere it appears—in numbers, and in alist[0], and in alist[1].

The solution is to not add the same list multiple times; instead, add a new one. For example:

def s_sort(numbers):
    alist=[]
    alist.append(numbers[:])
    alist.append(sorted(numbers))
    return alist

Now you've created two brand-new lists—one an exact copy of the original, one a sorted copy—and returned a list of them.

So, instead of returning [[3, 5, 7], [3, 5, 7]] (and also changing numbers to be [3, 5, 7]), it returns [[5, 7, 3], [3, 5, 7]] (and leaves numbers alone).

I have no idea why you expected [3, 7, 5] for the first element, but maybe you're doing some other work to the first element of alist which you didn't show us. In which case, as long as you do that work in a copying rather than mutating way (ala sorted(n) vs. n.sort()) or do it to a copy, everything will be fine.