I think, Roger is right, assuming, that BL5 should be updated to SW 3.X not the BS3...(?) But this depends on how old your BL5s are.
And for changing option setting to BL5 you must change the Link Option - L.OPT.
First thing - as always - disconnect BS3 and your BL5s from the mains (after setting it to standby mode), wait a few minutes and reconnect.
You said, BL5s green light comes up in SPEAKER 2 mode. What about SPEAKER 4 mode? And are they red in SPEAKER 1 - 3 - 5 mode?
Did you - or your dealer - assign the Powerlink ports correctly?
Next thing I`d try is to disconnect the front Powerlink out and connect it to your BL3s - Same fault?
Next you can try - connect your BL5s to the rear Powerlink...?
Next if your BL5s are daisy chained: disconnect both Powerlink cables (are they fully wired?) connect just one BL5 with one PL cable, then the second. - same fault?
Hope this helps
Stefan