Problem with Landlord charging rent while vacated from apt.

 Recently my landlord told me I had no choice but to move out of my apt. for 5 days so they could remodel it.  They wanted me to be completely out so they could paint, replace floors, install new appliances and blinds. They put a construction lock on the door during the remodel process and I had NO access to the apartment.
 While it was nice to have a fresh apartment to move back into, they want to charge me rent for the 5 days I was out of the apartment.  I feel this is not legal and I don’t see how they can charge me rent on an apartment I was locked out of for 5 full days.  Has anyone ever had this same problem with a landlord?  How do I prove that I do not have to pay for those five days?  Do I have a case here or not?