The information you are offering is not enough to even start a design. What are you trying separate from what ??
You need to try and get a hold of a book on oilfield production systems. This will give you a detailed procedure. But a quick brief..
Fundementally a liquid separator is vessel that allows a certain residence time that allows gravity spearation of two liquids (crude oil and water). This whole process is governed by Stokes Law.
Velocity of separation v is.
v = Kd2(density 1 - density 2) / viscosity2
Where
K = constant (gravity driven)
density 1 = discontinuous phase **
density 2 = continuous phase **
viscosity 2 = viscosity continuous phase
d2 = min. size of droplet to be separted (squared)**
The items marked ** are controlling factors.
Also required droplet spearation time = vertical height of continuous phase / separation velocity.
For gas and liquid the separator is a limited expansion vessel and allows the gas to flash off/from the crude. And then the above takes over.
2 phase separation is liquid / gas and 3 phase is oil/water/gas.
Horizontal separators give a larger surface area than vertical eqpt and this will help with separation and also emulsion handling.
A separator for free water knock out FWKO will take approx 75% of the water out, while a dehydration separator will take alomost 97-98% of water out of your crude stream. It should be clear this will be driven by physical parameters of your production fluids and the size of your vessel.
To help you out a bit. For your flow rate and provided it is a middle of the road crude with average water cut, a size of vessel you should be looking at to give you FWKO quality will be apporx 60 meters 2. Your rate of flow 5000 m3 /d is massive !