Well, the process is to send as a crossover submission, inside the SGC slab. PSA will evaluate it and determine what grade they believe it deserves. They then enter that into the computer and the person processing the order checks the PSA determination against the Minimum Grade you entered on your submission form. As in, if you want it crossed to PSA if it garners at least a 4.5, then you list 4.5 as the MinGrade you will accept. If for some reason PSA grades it a 4, they will return it to you still slabbed by SGC.
My advice: look at the card critically. An SGC 5.5 should have no surface wrinkles or creases, so that's a good place to start. PSA is pretty tough on corner wear, but at a PSA 5 level, all 5 corners could be nicked, but not enough to have surface creases. PSA cards grading at a 5 should have at least 85/15 front centering, which is pretty far off. It means one border can be almost 6 times the border on the opposite side of the card. Back centering of at least 90/10. If the card is miscut (meaning the card shows part of another card on the front or back), it would likely get the MC qualifier and detract approximately 2 points from the original grade.
PSA is also tough on "MINSIZREQ" meaning a card cut short from the factory, but not trimmed later, will still probably not get graded. So make sure the card is also the right size for the issue before you mail it in.
Post a picture of the card you're considering and we can give better advice if it will cross. To stay a 5.5, it needs to have some quality (usually centering) representative of a much higher grade. So if it's 45/55 centering on front, it might get a 5.5.
It's possible it could get a 6 from PSA, but I haven't heard of cards crossing higher without being cracked out.
https://www.psacard.com/resources/gradingstandards/