I sold an apartment owned for 10 years. The first 5 was rented and the last 5 was vacant. To calculate the cost basis, do I need to account 5 or 10 years depreciation?

You account for the depreciation while it was available for rent, vacant or not.  You should have been reporting the rental income, expenses and depreciation on a Schedule E with your tax return for each year it was rented or available for rent.

Thanks a lot for the answer; however things are a little more complicated. The property was available for rent only during the first 5 years. However during such period of time I was not a US citizen or resident (the property is located abroad)  and consequently I did not file a income tax returns in US. I stated filing income tax returns  in US when the property was no longer available for rent.

However during such period of (rental) time I was not a US citizen or resident

You're right. It's complicated. It only makes sense you would not have reported it on a U.S. tax return while it was a rental, since you were not required to file a U.S. tax return during that time. I would "HIGHLY" suggest you seek professional help for the tax year you are reporting the sale. You will need to seek the services of a CPA or other tax professional that is familiar with U.S. tax treaties between the U.S. and whatever country the property is in, as well as the country you are from. I seriously doubt the TurboTax software will be capable of handling your situation.