4-5 lbs is far too much

Average, healthy, maintainable weight loss is 1-2lbs per week
over the course of time. The lower your weight the less you will lose weekly. The higher your weight the more you will (probably) lose weekly. Everyone is different though - especially if you've got a sluggish metabolism from extreme dieting OR you dieted off a lot of muscle tissue (extreme diets do that!). If you start eating like a normal human again, your body will replace that lost muscle it requires to keep you alive.
My stats? Long story. Right now I'm once again at the upside. I'm also a "recovering" personal trainer and figure competitor. I dieted for 4 years. More than that if you can't the time I spent actually losing weight to get to my "healthy" weight. So, I've got some experience with this up and down crap & the mess it plays with the mind, self esteem etc - not only for myself, but my former clients. The story repeats itself over and over for most of us unfortunately.
When I trained for my competitions I averaged 1lb a week up until my final weight of 125-127lb. I'm 5'5.
The first time I lost a bunch of weight (before I messed up my metabolism with crazy low calorie diets) I was about your age. It took me 9 months to lose 72lbs. I started at 210lb. That's an average of 1.8lbs per week. I didn't lose that every week. Sometimes I lost more, less, none, or even gained.
Maybe not focus so much on scale but rather your body fat percentage & measurements, how clothes fit and your success with establishing the "healthy" habits needed to live fully at a healthy weight? I use a skin fold caliper to measure body fat percentage as I'm brilliant at gaining and losing water weight (as well as fat LOL)

The scale can't tell the difference between fat, muscle, and water. Sometimes I won't lose any weight on the scale but my measurements will go down.
If you haven't already, I'd consider working with a wellness or life coach. Someone who can help you with the "head" game, the self esteem & confidence you deserve to experience,
today. The reason I call myself a "recovering" personal trainer is because I realized that helping women change the way they looked in order to feel confident and worthy of self respect, is the EXACT reason so many of us struggle with self esteem, disordered eating, etc, etc.
I intended to help women but after a few years realized I was simply a part of the problem I'd intended to help women solve. There is zero reason, we shouldn't feel deserving of self confidence and self respect at ANY shape, size or weight. When we want to look a certain way in order to "measure up" to some externally defined image of "acceptable", many of us take extreme actions in order to get there - which as you well know, doesn't work long term!