The 40" version of the Samsung 5200 series 5, UN40J5200AF, does have a 3.5 mm (mini) headphone/speaker audio out jack. See the specifications here, http://www.samsung.com/ca/support/model/UN40J5200AFXZC/ ; just expand the section for More Specifications. This is also shown on page 6 of the e-Manual (expand the Manuals section). The direct link to the e-Manual is currently http://downloadcenter.samsung.com/content/UM/201504/20150417115111056/ENG-US_NMATSCJ-1.104-0410.pdf , according to my history.
I hope this helps. If you have a different TV in the series, check the specifications at Samsung's support site. There may be variations in the input/output options on the other TVs.
Cindy Wells
If you can download the software from Samsung website, put it on a flash drive. Plug into the computer. Run the program. OR, you may be able to download and install the software from Samsung website directly. Go here for more information:
http://www.driverscape.com/download/samsung-yp-t9
Good luck!
Try unplugging it for 15 to 30 minutes and try again. Mine did this last year and unplugging it got it working again. I had to reconfigure the settings again.