My puberty started around 17 and I am around 5'2-5'3.I am 20 now and I am 5'8. I still want to grow taller. Can I still grow taller. My mom is 5'4 and my dad is 5'11.

Most likely you are about as tall as you are going to get. You may have some slight growth, since it appears you started puberty fairly late.

At 20 you may not grow any taller, but there is nothing wrong with 5'8".My Grandfather was about 5'8" My Dad and my boyfriend are both 5'8". There stature speaks nothing about the tremendous men they are and were.

I would like to me at least 5'10