Try not to compare yourself too much to others. There may be some people who lose faster than that but I would say that is unusual, and unhealthy. Everyone's journey is different.
The question you need to ask yourself is whether you would have lost 10lbs, on your own, in 4 weeks? And would you sustain that into another month, and another, and another? Because that's how long it is going to take. You didn't gain 4 stone overnight, and you certainly aren't going to lose it in a few months. You also haven't managed to lose it through other methods and that's why you have turned to weight loss injections.
The jabs are going to help you to remain consistent and will support long term, sustainable weight loss.
For what it's worth - I lost 9.8 lbs on my first pen. I have now lost 60lbs in 32 weeks - that is 4 stone, averaging 1.5lbs per week and I've just dipped into a healthy BMI. I certainly would never have done that without MJ. If you had told me in November, that by the summer I would be 4 stone lighter I would not have believed you.
Of course there have been weeks where I have gained, when the journey felt like it was going to be too long and right now, it's creeping off me and I can't get down below the next stone. Yes it's frustrating at times, but I am 8 months in and have put in the hard work.
You are 5 weeks in, need to reset your expectations and realise that you are in this for the long-haul, develop some patience, and be prepared to invest in yourself.
It IS working, you just have to let it carry on working and not sabotage yourself by wanting it faster.