Panel Data Regression with Few Observations

I know very little of statistics but I need help to do my thesis. I'm running a regression with fixed and random effects in a panel data of 5 countries with 11 years of data. The number of variables I'm using are 5 and I need to analyze also a model with 6. Is this feasible?
If not, what approach could I take? I saw other papers used a broader set of countries to compare and put a dummy, but I do not understand how they do this. The paper I'm looking at is
Please, help me!! If you can commit to help me, send me a PM and we can see what I can do for you on exchange.

PS: I'm using Stata.