Hey,
I just got a brand new Inspiron 15 5000 directly from Dell and it doesn't detect headphones plugged into the 1/8" jack.
I've plugged two different pairs of headphones in and neither appears on the list if I go to control panel > hardware and sound > sound > manage audio devices > playback.
In both cases the audio on the internal speakers continues unchanged.
I went to Device Manager > Sound, Video, and Gaming Controllers > Realtek Audio right clicked and selected "update driver" and I was told the driver was already working on the current update.
One pair of headphones is a Sony mdr-7506 and the other was a pair of cheap earbuds. Both work fine with other audio devices