Microphone Latitude E5520

With this installation, I can use microphone and earphones, but if I remove the earphones, the speaker don't run.

The speakers worked okay before you installed the IDT driver? Open the Sounds properties (Control Panel>Sounds) and find Speakers/Headphones on the Playback tab. Make sure that under Speakers it says "default device".

If that doesn't help then try switching from the IDT driver back tot the Windows native audio driver by doing this:

1. Open the Device Manager (find it in the Control Panel, or type devmgmt.msc into the search box).
2. Expand the "Sound, video & game controllers" and right click on "IDT High Definition Audio Codec".
3. Select to "Update Driver Software".
4. Click on "Browse my computer for driver software".
5. Click "Let me pick from a list of drivers on my computer".
6. Put a check in the box "Show compatible hardware" if not already checked.
7. In the list of devices, click "High Definition Audio" (the native driver).
8. Click "Next".
9. On the Update Driver Warning box, click "Yes" (install the driver).
10. Restart the laptop if prompted. If not prompted, then no need to restart.
[To get back to the IDT driver, do it again but reverse the names in steps 2 and 7.]

If the speakers work all right with the native driver but not with the IDT driver then something in Win10 is preventing them from working.

=====================================================================

By the way, in certain circumstances the headphone jack handles different audio from what the speakers do.What I mean is, let's say you have the headphones set to be the "Communication" device, then when you are skyping or playing online games the communication audio will only go through the headphones, while only music or game sounds will go through the speakers. If that is what is happening, disable the Communication device, then all audio will go through the speakers or go through headphones when plugged in.