I live in FL and have 3 weeks before I graduate FSU. My landlord posted on my door a 5 day notice that states we have to move to another apt within the complex. The letter received states the new apt is available on Friday. My question is : after having received the 5 day notice, how long do I have to move all of my belongings to the new apt.

This is a longshot... but I'd say 5 days??

Move your stuff as soon as you can. You were given a 5 day notice. Call the complex manager and ask them when you can start moving your stuff.

Well first do you have a lease for the apartment you are in ?

My first call would be to ask them who is paying to move your belongings and when are their people coming to move you.
Sorry if for their benefit they want you to move, I believe they should be liable to pay for that move.