eviction vs end of lease

I am in a suburb of Chicago, Illinois. My tenant’s lease is up November 30, 2014. I told her that we are not going to renew her lease. Rent is due on the first of the month. When I contacted for the rent this month she said that she needed until weekend to get the rent together. (Which she has done in the past with a late fee) When I contacted her on Monday for the rent she says she doesn’t have it. So I asked how much does she have – she said nothing. So I gave her a 5 day notice. So my question is if I enforce the 5 day notice – how does this work out when her lease is up the end of November? Should I just wait until the lease is up? At that time can I enforce the holdover section of the lease?