I recommend boosting this achievement with a group of people. The more people the better, since it has to be done Online, the other players won't give you a chance and the AI is programmed to Expert Bots if you play Online, so doing it by yourself is really difficult.
This game is really anti-party chat. As if you even Private Chat with someone else the game registers it as a party chat and removes you from the game. As an alternative you can use exterior communication through some sort of Instant Messenger like Skype, Messages through Xbox.com, AIM etc. I did this in the map 'Lake' since the spawns are really close to each other compared to some of the other maps. We took turns having one person go to their spawn and kill all 5 people. You must do this as the CT team.
If you don't have 10 people, the people who are going for the achievement is recommended to have the Bots on the CT Team, since the AI is amped up there's a chance that the AI on the team who's suppose to get killed might catch the guy by surprise ending his streak. If you have 'no' other choice, as soon as you die press the X button and you will have control over a bot which will then make it easier. I have been told that switching guns or even switching to a knife has not allowed them to get this achievement, so you would want to kill all 5 members with your Primary Gun only.
Also, there is a reward for doing this same thing but on the Terrorist Team, so if you guys want to knock it out as well it will count towards you Awardist achievement.