My grandma left a 50K inheritance
You don't make clear where in the inheritance process you are. I actually know of one case where the executor (a family member, not a professional) distributed the inheritance before paying the estate taxes. Long story short, the heirs had to pay back part of the inheritance. So the first thing that I would do is verify that the estate is closed and all the taxes paid. If the executor is a professional, just call and ask. If a family member, you may want to approach it more obliquely. Or not.
The important thing is not to start spending that money until you're sure that you have it.
One good thing is that my husband is in grad school and will be done in 2019 and will then make about 75K/yr with his degree profession.
Be a bit careful about relying on this. Outside the student loans, you should build other expenses around the assumption that he won't find a job immediately after grad school. For example, we could be in a recession in 2019. We'll be about due by then.
Paying off the $5k "other debt" is probably a no brainer. Chances are that you're paying double-digit interest. Just kill it.
Unless the car loan is zero-interest, you probably want to get rid of that loan too. I would tend to agree that the car seems expensive for your income, but I'm not sure that the amount that you could recover by selling it justifies the loss of value. Hopefully it's in good shape and will last for years without significant maintenance.
Consider putting $2k (your monthly income) in your checking account. Instead of paying for things paycheck-to-paycheck, this should allow you to buy things on schedule, without having to wait for the money to appear in your account.
Put the remainder into an emergency account. Set aside $12k (50% of your annual income/expenses) for real emergencies like a medical emergency or job loss. The other $16k you can use the same way you use the $5k other debt borrowing now, for small emergencies. E.g. a car repair.
Make a budget and stick to it. The elimination of the car loan should free up enough monthly income to support a reasonable budget. If it seems like it isn't, then you are spending too much money for your income. Don't forget to explicitly budget for entertainment and vacations. It's easy to overspend there.
If you don't make a budget, you'll just find yourself back to your paycheck-to-paycheck existence. That sounds like it is frustrating for you. Budget so that you know how much money you really need to live.