my Windows Mobility Center does not give me all of those options... 

those are ky options..  Nothing about keyboard backlight

this answer does not fix my problem

I have an Inspiron 5759 / Windows 10 and do not have those options in control panel either.

Neither do I, I don't have that option as well.  Inspiron 5459.

I just spent two hours with DELL Support.  The 5000 series Inspiron Laptop's have no way to change the Keyboard background light time.. It is preset to 60 secs.  I was advised to update my BIOS, which I did and while it is now the latest one available, it didn't fix this issue. 

Asked and answered... 

I was surprised to find that no Dell agent got back with help with this.

I found the answer for my Windows 10 machine (or at least while the laptop is plug into Ac power) by booting into the BIOS.  Here's how:

CAUTION: Unless you know what you are doing, don't make any other changes. You could easily turn your inspiron into a brick.

1. Turn off the computer, and restart.
2. When you see the big DELL logo press the F12 key.
3. This brings up a list.  Select "BIOS setup" and hit enter.
4. Select "Keyboard Backlight with AC."
5. In the upper left check the check box that says "Keyboard Backlight with AC."
6. Click "Apply."
7. Click "Exit."

The computer will continue to boot and your keyboard light will remain on as long as you have AC power.

Thank you for solving this problem.  I, too am surprised that DELL tech was unable to provide this advice.  I followed your steps and ... sure enough... It worked and I am one happy computer geek again...

How do I change the time the backlight stays on keyboard with my INSPIRON 5558?