I will second getting all 5 at once. You might loose one or two to illness or predators and even if you buy only 2 and they both live you will have a hard time adding more later if you have a small coop. Because, honestly, chickens are cannibals and will pick on newer birds that you later add to the flock.
I have a fairly good sized chicken run and I will occasionally add new birds but I always buy them in "gangs" of about 5 or 6 because there will be some tension until the gangs work things out. Being that you can only have 5 and will have a smaller coop, it's just better to buy a single "gang" all at once.
Chickens are a blast and I love mine! I currently have about a dozen. I've been keeping chickens since I was a child and even so, I will occasionally loose a chicken to a predator or have a baby chick die (even though I feel very confident caring for them) so just plan that you might have a loss or two and count yourself lucky if you end up with 5 laying hens.
Speaking of which, you definitely don't want to go "straight run" or you will end up with 50% roosters. Buy "pullets." Sometimes a rooster accidentally get mixed in with the pullets too, so you might have to give one away if it becomes apparent you got a rooster at some point, but basically, pullets are sorted to all be girls, so pullets are what you want.
This time of year my Tractor Supply has baby chicks and later in the spring/summer they won't. But if they have them still when you are ready for them, you can buy your pullets at Tractor Supply and they will help you with what you need to start off with chicks. Like a feeder, waterer, chick starter, etc. Probably a heat lamp too, depending on if you get young chicks or not. But the babies have to be kept warm. I think that is probably the #1 think you can do to ensure the survival of baby chicks is to make sure they are warm.
Good luck and have fun! Chickens are a blast. If you handle them a lot growing up they can be very tame and have fun personalities.