More direct follow-up hint:
In order for you to get the fourth digit, the fifth question must indicate exactly one number, and only one number. Because it is comparing a sum to itself, the only way it can isolate a single number is at either end of the 1-9 set, if the total of the other three numbers is either less than 2 or greater than 8.
Even more direct hint in next comment.
Even-more direct follow-up hint (with one number worked out):
If the first three numbers are all 1 (as low as they can be) and the fifth question is false, then their sum is 3 and the fourth number is either 1 or 2. Because that doesn't isolate a single number, that can't be right - so the fourth number must be 9, with the fifth question being true and the sum of the first three numbers being 8.
From here, the rest of the solving should be a lot easier - there's only so many combinations of the numbers on this phone that can total 8!
Thanks for this! I got the right answer but was a little confused as to why my order was correct. Your comment that "there's only so many combinations of the numbers on this phone that can total 8" set my mind at ease that there isn't a clue necessarily for the correct order, but that a few different guessing attempts are allowed.
