At 5 ft tall and 165 lb your BMI is 32, which isn’t too bad; the ideal maximum healthy BMI is 25 (as recommended by most health authorities).
To achieve a BMI of 25, you’d need to weigh 128 lb, whereas your stated target weight would take you to a BMI of 22.5.
I’ve calculated that an average person needs a daily calorie intake of 15 calories/lb of weight (or 33 calories/kg of weight) to maintain that weight. So by my calculations, you should consume 1650 calories/day to reach and maintain your ideal weight of 110 lbs.
My advice would be to consume that 1650 calories, which will take you to your idea weight reasonably quickly and you will be consuming your future normal calorie intake to maintain that weight.
The BMI is calculated from your weight (in kg), divided by your height (in metres) squared.
The BMI is a fairly crude measurement, to my mind a much better indication that a person is not overweight is that your waist circumference should not be greater than half your height.