Tenant eviction - tenants claiming health issues in rental

[Jan Vandenberg]

My tenant has provided a 30-notice and will be leaving at the end of May. The lease expires end of July. This is a friend-of-a-friend situation where we allowed them to rent without deposits and upfront rents to help them out. I have no issues with them breaking the lease however I am fairly certain they will not be paying the last month’s rent (May) and haven't paid yet. They are complaining about mold issues in the home and holding health issues over our head. They had an air quality test done in Jan 2019 but didn't share any info with us until late April. Nor have they complained previously about health-related issues because of the air quality. My philosophy is I can't fix it if I don't know about it.. 
 

I'd like them out, don't necessarily care about the May rent but I want them to know what is due to us.  Should I send them a 5-day notice to pay or leave? I'm afraid if I don't they may hang around in June too. Just don't want future issues... 

Advice anyone?