Hey yeah getting your credit up can be a journey. I know for a while after graduating and paying off debt I saw my score moving up but for whatever reason it kind of just plateaued. Looking at my report I realized that I was still on my moms card who had just moved and had debt.
1.While being on someone else's account can help you your score gets weighed with the debt that your grandma has so yes paying that off would help but unless that's something you are feeling is the right choice or are in a strong position to do that maybe hold off. The only way I got it off my report was to have my name taken off her card but you may need able to call and negotiate with the credit bureaus or see what a credit repair specialist says.
2. It may crazy but sometimes closing an account can harm your score too. Credit utilization is how much credit you have on balances in regards to your limits. You said 4-5k in balance. Well if her credit card limit is 6k then your utilization is 83% which is high. Usually lower utilization helps your score more I've seen people say between 10% and 30% but having a 0% utilization from closing can also be bad because you reduce your available credit.
3. Think about getting a secured credit card. These are designed to help people who are building their credit. Pretty much you pay a set amount and then that counts as limit like a debit card. Then you could always consider having your name taken off your grandma's card.
Credit repair can also help if you are ha ing trouble.