Can I tow a 4000 lb. trailer in 5th gear (auto) safely?

Maximum towing is 6500pds so you should be fine.

Max towing capacity is 6500 lbs WITH the towing package. But without the tow package, you should be fine. I
would put it in 4th actually around town so that it doesn't shift by itself a lot. Easier on the transmission.

If you have the tow package (with oil and tranny coolers) yes. Just pay attention to what gear it's in. If it's hunting a lot, drop down to forth. On flats and down hills you should be fine. I can tow 6000lbs with my manual in 6th just fine most of the time. Just down shifting for hills or to accelerate.