Yes, if not the only way. Your issue is not uncommon but slightly complex, and you'll need to hire an attorney familiar with both areas to navigate the legal waters. It may not be too late, depending on the circumstances. Good luck!
You would definitely need an attorney. While it is possible that the sentences could run concurrently, you are quickly running out of time if there is only 5 weeks to go on the sentence in Washington County. He would be to get on the docket in Sullivan County so that he could begin resolving the matter. The first step would be to hire an attorney as quickly as possible to get the ball rolling.
This communication does not create an attorney/client relationship. My answers are intended for educational purposes only. No action will be taken on your behalf without a written retainer agreement. I am licensed only in Tennessee. Therefore, if you are outside the state of Tennessee, it is recommended that you consult an attorney in your jurisdiction.