In this style I find it's useful to stick to a finger per fret so for the A7
shape I might use a different fingering in other styles of music.
An alternative name for an A5 chord would be A(no3rd) - so you can see that the A7(no3rd) is the same chord with the added 7th note.
This chord may take a bit of work to get but the sound of it makes it worth the effort.
I have tabbed out the "moving A chord up the neck" riff that I play at the end of the video.