Howdy and Welcome to Chordie!! I'm sure one of our banjo playing members will chime in with something more useful, but I think you can get your F with a one finger barre at the first fret ( 1111 ) and Am at the fifth fret with three ( 7557 ). If you find a tune that you like, over on the song page you can choose 5 string banjo for tuning, and if you click on the chord chart in the upper right corner of the chord you want to change, it will show the variant fingerings for that chord. You may then print that song with your preferred chords displayed for study and practice.
Hop into the forums, ask questions, comment as you feel, and make a few new friends here in the Chordie Community. A nicer group of folks you won't find anywhere else on the net!
Take Care, and Again Welcome!
Doug
"what is this quintessence of dust?" - Shakespeare