Air conditioning with exhaust fans between two rooms
First, "recommended"? Coming from a contractor and engineer, it sounds like a good solution, and it will work.

You don't need two fans. One with a transfer grille will do.

Power-wise, I have to this in IP so bear with me. Room 1 is 5 x 7 x 3.28 x 3.28 = 376 ft^2. Rule of thumb- and this is only an estimate - is 400 sq ft \ 3.5 kW. (1 ton refrigeration = 12000 btuh = 3.5 kW). It could be 600, but you would need to know construction type, insulation, fenestration, exposure, latitude, etc. and consult ACCA manual J. With high humidity, you want to make sure it runs long enough to dehumidify. Now add the second room which is 14 sq m = 150 sq ft. Total area is 527 sq ft. Using our rule of thumb, that would be 527 sq ft x 3.5 kW\400 sq ft = 4.6 kW of cooling. If we assume 6 air changes per hour (another rule of thumb), the volume of both spaces is 147 cu m or 5187 cu ft. X 6 air changes = 31,123 cu ft per hour which is 518 CFM. Again, rule of thumb is 400 CFM per ton, so 518 \ 400 x 3.5 is 4.5 kW.

So your exhaust fan should provide a minimum of 14 x 3 x 3.28^3 x 6 \ 60 = 148 CFM or 4.2 m^3\min. 

Size the transfer grille for a maximum 500 ft\min, so about 42 sq in. A6 x 8 will be quiet. Probably quieter than the fan.