I am doing a fixed effects regression with 5465 N and 5 T on Stata. I have used the fixed effects regression model and used the code vce (robust) to account for autocorrelation/heteroskedasticity. I spot no multicollinearity and as I know the residuals do not play such a big role if N is so much bigger than T. Also there is linearity in the regression. Moreover, I receive a within Rsq==0.54 and a Prob>F=0.00.
Does it mean that I can use this model?

It is really important for me as this is a part of my master thesis. I would be grateful if I could get any replies