I think you are being unrealistic and your target is actually an unhealthy weight for someone your height, especially if you are going to be building muscle by exercising. More muscle is good as it boosts your metabolic rate.
When I was a student, I was the original 8-stone weakling. Then I started playing football regularly and weight and circuit-training and put on almost 2 stone and would lose a few pounds in the summer when football stopped. When I got too old for football, I got into athletics fairly seriously, running several marathons and was seriously fit until I burst a hamstring playing 5-a-side in my mid-40s. I never got back to the same standard, but I've never stopped exercising.
I'm now 70, 5'6" and still fit a 30" waist trouser, as I did when I was 21, and I'm not on any medication. I haven't weighed myself in years, but I'm probably still round about the 10st mark, or just over, as my stomach is still pretty flat. I've cycled just over 1100 miles this year so far, and I'm looking forward to getting back to golf again tomorrow. I eat too many biscuits and have the odd glass of red wine (medicinal) and, maybe a couple of times a week, a pint of stout.
No special diet, no self-denial, just a sensible diet and lots of exercise - 30 hilly miles today.
Long-term health is achieved by eating a healthy diet, in moderate quantities and getting plenty of exercise. Do that and everything else takes care of itself.