How hard is the AP Gov exam?

Is it possible to take the exam and get 5 through self learning? Any online course recommended?

Yes, using whichever of the usual test prep books suits you best.

Whether it’s worth doing relates entirely as to why you are doing it in the first place.

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Most universities do not recommend self-studying of the AP exams.
They want to see grades in a classroom.

Additionally, your previous posts indicate that you are targeting top schools.
Based on your questions and comments, your written language skills are going to impact your admissions. If you have time to self-study, please work on your writing skills.