in what basis the size of hole and fastener to be selected

If am having writing board 5ft x 5ft and of thickness 1/2 ft. it is weighted of 5kg.
should mount it in a wall. in what basis i should make a hole in wall. technically

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A fastener of a given diameter and material will have a published shear strength if it is an actual graded fastener. For a small screw that might be used to hang a picture or board, I doubt you'd find one that comes with published material or strength properties.

Anchors that are used in walls will have shear and pull-out ratings listed by their manufacturer.

All of these properties are "best case" scenarios. Defects, installation, and other mistakes will reduce the capacity, so you'll want to me factor of safety applied.
For a board on a wall, a factor of safety might be 3. If you were instead suspending the board from the ceiling, and people would be walking under it, then you would use a FOS of 10 or possibly more.

 
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The fastener it might be sized according its strength under that kind of weight. So some simulation it may be taken with SW.
But in the other hand is the wall consistency. If is just clad or hollow bricks made then the evaluation is doubtful.

 
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5Kg is pretty lightweight. Simple items you might use to hang framed art would work fine.

As fulvio mentioned, a lot will depend on what the wall is made of. Another factor is what you can do to the wall. Drilling and mounting anchors is nice, but it leads to holes in the wall that may need to be repaired one day.

If it is a soft wall, look at something like these:https://www.amazon.com/Picture-Hangers-Overfly-Hanging-Mounting/dp/B071LKJWK3/ref=sr_1_11?ie=UTF8&qid=1509662030&sr=8-11&keywords=picture+hangers

I can't imagine any reason why a simulation would need to occur to hang a board on the wall :)

 
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