Reading switches without a common ground from Arduino
Hoping that only one button will be pressed at a time, I have a software solution based on polling :

Let A is connected to Pin1, B is connected to Pin2 and so on..


  First configure Pin1 as output port and all others as inputs. And out
  a logic '1' at Pin1. Read the values at Pin2 to Pin6.
  
  
  if Pin2 = '1' then SW1  is pressed.
  if Pin4 = '1' and then SW5 is pressed.
  


Now repeat the above steps with Pin2 as output port and others as input ports (Change the conditions accordingly). 

EDIT: As Spehro Pefhany commented, this will work for upto two switches pressed simultaneously.