I think you actually need to get ALL the kills from w/e weapon you're going for in a row. So since you got the claymore in between, it "reset" so it only counted 3/5 kills.
I may be wrong about this and I've had trouble with this before but I tried using ONLY the weapon I was going for and it worked for me.
I just got a Blood Thirsty for:
1) Ballista Sniper kill
2) Ballista Sniper kill
3) picked up an enemy PDW57 (1 kill)
4) Ballista Sniper kill
5) Stole an Enemy Lightning Strike care package (2 kills)
6) Ballista Sniper kill
7) Ballista Sniper kill
Then i got killed.....
So Ai-Silentshot i think you are incorrect.
I wish a Developer would respond, or someone that knows FOR SURE how the BloodThirsty for skull camo works.....