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Im 23 and weight 125lbs been holding the same weight for over 5 years no matter how much I eat or dont its the same.

Ditto, but hey it's magic, I aint gotta explain ****

Increase meat in your diet and start doing some sport. Go to the gym, swim, or go running (well it would be best if you do all of those :D) it will help you to gain muscles and therefore weight (muscles are heavier than fat). It will be hard in the beginning, it always is, but don't lose faith (it takes cca 1month for you to notice that your body is changing), shoot photos of yourself to see that you truly are gaining muscles. Get a good workout routine (plenty of them on the internet). Just don't sit the whole day at home (not just because you think you are skinny which doesn't really look healthy, but think about how unhealthy you can become if you continue like this).

Do you think if I do around 75 push-ups and 150 sit-ups, I will notice difference?

you might notice a quick tone up but it will go away as quickly as it came because you will plateau. remember, high weight low rep for bulk (gain weight) and low weight high rep for tone (lose weight).

you will for sure but it will probably take longer. Don't forget about other muscle parts too such as your back and legs, I can't really imagine someone with a big chest and shoulders and a small back... look up some exercises you can easily do with your own body at home (i would recommend you something but i got no idea how they are called in my own language :D)

ok thanks