What kind of generator do i need to run a 1.5 or 2 ton Air Conditioner?
Power Consumption and cooling capacity. Which one determines the value I am interested in? For an Air conditioner of 1.5 ton ,the power consumption is 1438 wattt and cooling capacity is 5,050 W.


Your air conditioning unit works on the principle of a "heat pump". In your case electricity is used to drive the pump. According to the rating plate it will consume 1,438 W of energy while pumping 5,050 W of heat. It is common to quote the coefficient of performance (CoP) for heat pumps as \$ \frac {heat~moved}{electrical~input} = \frac {5050}{1438} = 3.5 \$ which is reasonably good.

The generator is rated at 5 kVA. For a purely resistive load 1 VA = 1 W but your air-con unit will be an inductive load so we'll need to derate the generator by about 20% when converting to watts. Let's go for 4kW.

Your 1438 W AC unit (let's call it 1.5 kW) will load your generator by approximately \$ \frac {1.5~kW}{4~kW} = 38\% \$. It should be fine.