Any system with INTEL Graphics requires the driver to use more than 1 monitor.

Do you use the VGA port? 

Looks like you have onboard DP, HDMI and VGA. Do you use 2 monitors? What ports are on the monitors?

If neither has HDMI, you could use an adapter for HDMI(PC)>DP(monitor) or HDMI(PC)>VGA(monitor) for one of the monitors. Keep in mind that these cables only work in one direction so make sure you get one that's HDMI(PC)

You could try clearing BIOS:

1. Reboot and immediately press F2 to open BIOS setup
2. Copy down all current BIOS settings, to be safe
3. Power off, unplug
4. Press/hold power button for ~15 sec
5. Open case and remove motherboard battery (Check Service Manual for details)
6. Press/hold power button for ~30 sec
7. Reinstall the battery (Time for fresh CR2032 3-volt coin cell battery? ~$2.00)
8. Close up and connect mouse, monitor and keyboard
9. Reboot

questions not asked, then not  told , and not your fault, mine.

what country? (20.20) UAE with VGA and is a MICRO.

what are you trying to do with it, tell all you intend to do first. and what fails.. exactly using what.

what monitor make and model are you using, and if 2 monitors? tell that, and if using DP extended mode.

are you attempting to do 2 monitors at the same time.?

are you connecting 2 video cables,? at the same time?

we can not See your PC (yet) nor know what is connected to what, no can do. not yet. but see do see 1 photo.

My wild  guess, is this you have UAE custom BIOS,  does the F2 key work with only 1 VGA monitor attached?

My guess is that the BIOS in this PC is UNIQUE and must be set to the desired, video port you want to use.

if not DP, you must tell  the BIOS I want to use VGA.  Might be called Legacy VGA inside. BIOS.

do not have DP monitors connected at the same time you try to use VGA< just 1 cable

and no funky video adapters here.

(how ever a DP to VGA are sold and work great, bought with great care and direction DP >>VGA)

that is all I can think of on VGA, on any non USA PC.

I now found the correct MICRO book and it shows the VGA here,

so is this card there, and is the cable seen here seated properly at BOTH ENDs.

does the card show up in F2 BIOS screens. dell has no BIOS book for this PC so, one can only guess what is there. F2 (wise) This is in the 2018 year book, my book is too old and does not cover this.

Even i used the VGA port only still facing same issue (no display)  

what monitor do you have..  modern new ? or year 2000 made.?

have you flashed the BIOS?  on this PC what version of BIOS is yours.

@hameed1985  - Did you try resetting BIOS like I suggested above?  Can you test this monitor using a VGA port on another PC?  Is anything marked with an X or ! in Device Manager, or is there an "Unknown" entry listed in Device Manager?

Assuming this is Windows 10, you can try reinstalling these drivers, in order, if resetting BIOS doesn't help:

1. Intel Chipset Driver 
2. Intel Management Engine
3. Intel UHD Graphics Video driver

And if none of that helps and this PC is under warranty, contact Dell Tech Support.

@savvy2  - The Optiplex 5060 Micro has no x16 slot on the motherboard. It only has on-board Intel video according to the specifications. So there are only onboard VGA, DP, and HDMI ports for Intel UHD Graphcis on this PC.

@RoHe 

i have reset the BIOS (not working) and re installed all 3 drivers , still same issue VGA port no display .

when i remove and reconnect VGA cable is shown in the monitor entering save mode tired it with different monitors same.

only the DP port is working .

monitor entering save mode happens whether there is a pc or not.  Display port to vga is specific connection and its not bi directional.

Models with Display port don't usually have onboard VGA ports.

https://www.dell.com/support/manuals/us/en/04/optiplex-5060-desktop/optiplex_5060_micro_service_manual/working-on-your-computer?guid=guid-9ccd6d90-c1d1-427f-9e77-d4f83f3ad2b6&lang=en-us

ONBOARD VGA is optional.  It  also does not work without drivers.  its not native to windows.

https://www.dell.com/support/manuals/us/en/04/optiplex-5060-desktop/optiplex_5060_micro_service_manual/optional-module?guid=GUID-210151B9-A69D-414F-85B1-3585A5041F38&lang=en-us

name the monitor make and model please.

show photo of YOUR VGA port cover off so I cans if the optional card is there or even not ribbon cable connected fully,  hardware matters,first, or all software will be dead .

is only the 1 VGA cable used, no others, use  only 1,cable please.

MONITOR shows power saver mode.

that means the video or video syn wires in the VGA cable are dead,  RGB and or H_sync or V_sync pins are dead.

when any monitor sees that it goes to power saver mode, why waste power if PC is dead or the VGA port is DEAD, sure it does not it is ENERGY STAR RATED to do just that .

so the VGA port is dead, next is what, open case see if the card is there, not damage, LOOK at it then look  at that cable to the tiny side card, and that both ends of the cable are in fact connected correctly and fully.

the using DP monitor , only one cable used, to DP port, no others, power  on PC and hit f2 hammer it gently

and gain BIOS screens in DP, the find video page and set it as you want.  if you  want VGA pick VGA< the save BIOS and exit BIOS and then test VGA.

there is plan , if that works windows then works, but only if the above are correct, Best I can tell , dell has no BIOS box on this MICRO.

Where's the PCI-e x16 slot??