Hi Holly

Your BMI is 23.6, so already in the healthy range. Your target weight would put you at BMI 21.1
This means it will be much slower for you to achieve than for someone overweight losing those 15lb. You probably also need to be quite strict about cutting down on alcohol and any sweets, cake, bix
People sometimes binge on 4:3 but not 5:2, in which the rate of weight loss may be the same. So, you could try 5:2, possibly with a mini-FD of up to 1000 cals.
However, the main reason you are tending to binge is probably that you are trying to restrict yourself to 12-1400 on NFDs, which is far too low for most women of 5'6" to be sustainable.
5:2 / 4:3 lose weight on FDs; NFDs are NOT supposed to be diet days and a big contrast FD / NFD is important.
You need to calculate your TDEE (Daily Calories to Maintain) which is the aim on NFDs
On 4:3, you should aim for this on NFDs
On 5:2, some folk speed up weight loss by eating at 20% below TDEE on 3-4 NFDs, so the full TDEE at least one day per week.
As an example, with your height, weight and activity level (classed as light) your TDEE would be1900 at (example) age 35.
At that age, on 5:2 you should eat 1900 cals at least once per week, but could go down to 15-1600 cals on 3-4 days. On 4:3, aim for 1900 most NFDs.