Hi and welcome to Just Answer!
The question is - was the property transferred to you when your mother was alive (gift) or you became an owner as a result of her death (inheritance)? Based on your information - your mother gifted the property back in 2005 - thus you have the same basis as your mother had at that time (purchase price - assuming the property was purchased plus improvements and some other expenses during the time she owned the property). You will add improvement expenses after 2005 (since you became owners).
The fact of registering the transaction after her death makes no difference for the fact that the property was gifted. However local authorities may assess additional property taxes if your mother claimed any property tax reduction based on her ownership while the property was actually gifted to you.
If the property were inherited – means you become owners based on her will or through the inheritance law as a result of her death – you might have a stepped up basis equal to the fair market value of the property.
Please also verify if the quitclaim has a "life estate" provisioning? Let me know if you need any help or clarification.