sory wld ,its not quite a c shape at 5 fret.,its second string 5 fret,third string 6 fret,fourth string 7 fret.
if you make a c7 shape at third fret you have d7 plus 9,sometimes can be used instead of d7,the same shape at 5 fret is e 7.
b7 shape at 6 fret gives you another e 7,there is a two fingered e 7[modal] at 7 fret fifth string and7 fret third string EEDDBE,All this is standard tuning so you have three chord trick all around fifth and seventh fret,lots of options for e 7,and an alternative d major chord ist string5 fret,second string 7 fret, third string 7 fret,http://www.dickmiles.com