Chicago Late Fee, Partial Payment, and Five Day Notices

[Frank S.]

Howdy,

Tenants thew a party, bought furniture, and now are a little short on cash, go figure.

I am double checking a few things, can a Chicago expert please confirm this information?

2017 Chicago Residential Lease

5. Late Fee. The Monthly Rent shall be automatically increased $10, plus 5% of the amount by which the Monthly Rent exceeds $500, as additional rent, if received by Landlord after the 5th of the month for which it is due.

Per this, I can collect  a late fee AFTER the 5th and the late fee is the same the same no matter if they made a partial payment.  Can you confirm, please? 

E.g., $1,325 per month, fee is $51.25.

LANDLORD REMEDIES {MUN. CODE CH. 5-12-130}

If the tenant fails to pay rent, the landlord, after giving five days written notice to the tenant, may terminate the rental agreement.

I read elsewhere that if you accept a partial payment, you should send another 5 day for the amount due.  Otherwise, this is case will be thrown out in court in Chicago.  So, if  I send a 5 day on day 3 and then they don't pay after day 6, I would have to send another 5 day to include the late fee?  

 Thanks, 

Frank