Can a parent give a $13,000 gift to a child and not have that money count in a 5 year look back by the IRS?

Pokagon - well this is a big gray area isn't it!. Mom can gift you whatever and those $ fall under IRS rules. But Medicaid looks at $ gifted or transferred differently and can do a transfer penalty based on the amount "gifted". What our attorney suggested was to get a "personal services contract" done and the $ paid via the contact is income and 1099 reportable. But by doing this it won't be an issue (or well it shouldn't be if the legal was done correctly) for Medicaid later on.
imho you kinda need to figure out how much you're looking at for an IRS penalty vs a Medicaid transfer penalty and which is worse or easier to deal with should it become an issue. Whatever the case, you really need legal done by an elder care or estate attorney. Good luck.