Yes, based on your height and weight, you should be able to comfortably ride a Royal Enfield Classic 350. The Classic 350 has a seat height of around 800mm (31.5 inches) and weighs approximately 192 kg (423 lbs) in its standard configuration.
At 5'6" (168cm) tall, you should be able to reach the ground comfortably when seated on the bike, allowing you to maintain stability and control at stops. The weight of 65 kg is well within the typical weight range for riders, so you should have no issues handling the bike.
Everyone's body proportions and preferences are different, so it's important to personally assess the ergonomics and make sure you feel comfortable and confident while riding the Classic 350.