Renter is breaking lease 5 months early.   They want us to pay half of the realtor fees to list/show our rental property when they move in 2 months.   We have declined to pay anything for this service.   

What we think is reasonable as landlords (state of Ohio) is to call local colleges, prepare the craigs list ad, call local network for renters, etc..   But paying a large fee to realtor in a highly rentable area long before I had planned to re-rent the property is not reasonable.   Thoughts?

Agree that you do not want to split a cost of something you would not normally incur.  Odd that they would even suggest that, but feels like they are trying to get off easy.

Do you have a penalty for breaking the lease built into your lease?  Forfeiting the deposit is a good penalty.  What does the local tenant-landlord law say about breaking leases or maximum fees?

They should me on the hook to pay rent until a new tenant is found and pays rent, if you are making a good faith effort to get it re-rented.  We sometimes split the loss with tenants if they get out quickly and we have more latitude to show the unit to get it re-rented.  If it is empty for two weeks, we each get stuck with a week of it.

Be fair but be firm.  Encourage them to leave, then the risk of damage, non-payment for time occupied, and chewing through the deposit is reduced.

Get them to cooperate with showings. Start advertising now and you should be able to find a new tenant to move for when they move out. There is no reason in a situation like this that you should experience a vacancy. 

Have them pay your costs to advertise and screen new tenant.