Because Bamber was determined to get his hands on the dosh that Daniel (and his sibling) would have been in line for.
Why five shots in an arc though? Why not two or three random shots in different parts of the head?
Was he trying to leave a hit-man type signature, Curiosity?
Nah!Sheila was the one in a trance like state, simply standing there firing shot after shot, moving the barrel slightly each time!