I'm also 5'3" and a few years ago went from 12.5 to 9 stone 10 without starving myself and doing weights and HIIT in the gym.
It's about eating (and exercising) smarter, there's no reason to starve yourself if you can eat more! A higher % of muscle means you're burning more calories just existing and gives you a better shape (Imo).
For example I'd eat:
Meal 1: 5 egg whites with 1 whole egg omlette, top with spinach or mushrooms or peppers
Snack (choose 1):
Greek yogurt
Tina of tuna
Tin of mackerel
100g smoked salmon
2x ricecake peanutbutter or almond butter
1 hard boiled egg
Meal 2: 2x 150g Turkey burgers with 60g sweet potato, greens (either broccoli, spinach or asparagus - small handful)
Snack (choose 1):
Greek yogurt
Tina of tuna
Tin of mackerel
100g smoked salmon
2x ricecake peanutbutter or almond butter
1 whole hard boiled egg
Meal 3: 250g chicken, 5 egg white scrambled, 60g sweet potato, 75g broccoli
Be in the gym 3 or 4 times per week doing weights e.g. and 3-4 times HIIT (High Intensity Interval Training) of 20 mins (I'd usually do this on the treadmill or stepper- run flat out for 20 secs then stop for 40, repeat - this apparently keeps your body from getting used to the activity level)
Quads/Glutes
Leg ext. 3 sets of 20 reps to warm up. 5 sets - 5 normal, 5 hold for 3 seconds, 10 normal.
Goblet squats, 5 sets of 15.
Leg press. 6 sets of 30 reps, wide feet. 3 sets of 30 close foot.
Bulgarian split squats 4 sets of 12
Glute Bridges 4 sets of 15, SQUEEEZE
4 sets of weighted walking lunges to finish w/ 4 sets on prowler
I was a size 8-10 and have never been fitter or looked better imo in my life.