You shot these at ISO 1250 which is a pretty high ISO for your camera and you are always going to see more grain at high ISO numbers. The second reason is that the face is underexposed and underexposed areas of a shot are going to show more grain. Considering the two grain causing reasons the shot looks pretty good.
Lower the ISO to max of 400 and use flash fill to light the face and see the difference
I also have a D5300 like the OP.
I remembered setting my max ISO the other day, but forgot what I used, so I just checked it and was surprised to find it at 12800.
I thought this camera handled high ISO better, but I am early in the learning process.
As a fellow newbie, the OP will want to know that these settings are only available in P, S, A and M modes.
On any of the auto modes, this option is greyed out and I assume ISO reverts to full-range auto.
I noticed on my D5300, when I set the max ISO to 400, the camera defaulted to a minimum shutter speed of 1/60.
I felt that was a bit limiting, so I changed it to 1/40. Not that I have the steadiest hands in the world.
BTW
arsudarsan, here is the menu direction to all of this:
Menu
Shooting Menu
ISO sensitivity settings
[I assume] ISO sensitivity
100
[I assume] ISO sensitivity control
ON
Maximum sensitivity
400
Minimum shutter speed
1/60 [camera default]
And yes, with more light on that beautiful Indian skin, the better your results.
This is a wonderful forum with which to learn, and you will get much encouragement to leave the auto settings behind, and to study up (Google) on the exposure triangle (ISO, aperture and shutter speed).