I have an Inspiron 5559. I cannot get any audio from the speakers in the laptop, but whenever I plug in headphones the audio is fine. I have updated windows, updated drivers, uninstalled and reinstalled the driver, made sure nothing on the computer is muted, etc. And it does not still think the headphones are plugged in. (Also, the speakers were working fine last time I used the computer, but I had to take it to a tech guy to get the power jack and the palm rest replaced. When I got it back and turned it on, the sound wasn't working. Could it be that he did not plug the sound card or something in right? But then why would the headphones work?).
You might need to switch your sound system from HeadPhone to speakers, right-click on the speaker icon on your taskbar for settings.