Tenant did not pay final month’s rent

[Steven Cherry]

Hi everyone.  I have a tenant that’s supposed to move out at the end of this month.  Rent was due on the 1st with a grace period until to 5th.  Then a late fee hits and he lease says I would start eviction if not all received by the 10th.  I know that I should try to get rent and not take it from security at the end, being that if there is a ton of damage, security may not cover it all.  I believe eviction takes some time and costs a bit.  Would it be worth filing on the 11th if they are supposed to be leaving the 28th?  They asked if they can stay a couple extra days after the 28th and I said no (I plan to touch up and rent ASAP).  Between not paying rent, potential damage, and potential for them to stay in there a few extra days, I’m a little worried about not taking the right action now to cover myself.  Any advice?  Thanks!