This is probably the easiest out of six "Complete 5 missions with X squad member" achievements as it's related to your missions with Kaidan Alenko, who is the first companion to join your team. Simply keep him in the party after Eden Prime and some early recruitments on the Citadel, and the achievement will pop-up quickly.
Of course, if you want you don't have to do it immediately as the achievement doesn't need consecutive missions. Just 5 total in the whole game, but if you are new to the series, it's advised to them before the Virmire story point.
Assignments counts as missions.