I have tenants that with a lease expiring at the end of May.

This issue of possession has critical consequences to expiration of judicial redemption rights, curing a void tax sale, and avoiding short statute limitations that allow the taxpayer to regain the property without paying the investor anything at all.

It states: Landlord hereby grants to Tenant the option to extend the term of this lease for an additional period of five years, commencing when the prior term expires, upon the same terms and conditions as are provided for herein.

But did end the lease as of October.So now I have a person with an expired lease.

Negotiated a price under market value and will raise rents to market value when the current lease expires.

Would assume the zoning won’t ‘expire’, can always check with the city/county on that.

However, I do see how a small business can forget to pay for their yearly registration with the state for sunbiz (they expire in Sept. if you haven't paid).

You can terminate the lease at lease expiration by providing the proper amount of notice (which you gave sufficient notice).As has been stated, this is a tenant friendly state and San Diego is a tenant friendly city. 

The tenants are on month-to-month with well expired rental agreements.

Current lease term (expiration date, month-to-month)7.