If you put your 1st finger on the 5th fret, this would
be an A13 chord (or an A7 with and added 13). Since there
are not any open strings, you could play this chord anywhere
on the neck. The root (letter name like A) would be whatever
the name of the note is on the 6th string. This chord
can be used as substitution for plain old A7 chord when
a more "jazzy" sound is desired.