May I know which software you use? Eviews, STATA, or Gauss?

I am not clear whether your p-value refers to your F-statistic. If so, the second case will not happen. Again, I need to know whether your p-value refers to the joint significance test associated with your F-statistic.

Thank you.

At first, you need to know the purpose of F-test in your case, i.e what's the null hypothesis H0 and What's the alternative hypothesis H1.

Your results (F>Fc or p<0.05) show that the test statistic is singnificant in 5% level. I.e the H0 is rejected in this case.

Under same singnificant level such as 5%, the results F<Fc and p<0.05 are impossible.

Use your pencil draw a pdf of some F, shade the tail area 5% at the upper side or on both sides... Then figure out where is the p where is the CV. It has nothing to do with software, any, at this stage.