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Need direction on refinancing my mortgage

I took an 30-year FHA home mortgage 5 years and 2 months ago on a 208,000 home, at the time I just paid for the closing cost and had 0% down payment (not something im proud of), also my credit score wasn't great at all, so imagine that, to put it in perspective, I'm paying 1466 a month for it and now I know my interest rate is 7.57% on the loan.

All this time I just made sure I pay on time and never miss on payment, which I'm good here, suddently I started getting letters upon letters from different banks about refinancing my home. I grew curious so I started to investigate more. I found out that the average interest rate is somewhere between 2 to 5.5% for the home, whichs puts my interest WAY but WAY too high.

5 years later, I have paid 11% of this loan and I'm thinking about saving money. Now I bought this home 5 years and 2 months ago at 208k, the home value today is around 260-265k give or take. I'm not sure how real state works here.

11% paid of this house is $20,000 give or take, so I have 20,000 equity...? right? Now my house value went up to by $52,000, is this also equity or what happens to the 52,000 that the home value went up by. Is this own by the bank or is it my money?

This is the real state number I don't understand.

EDIT: my current credit score is 751, which transunion and equifax rate as "Excellent"

EDIT2: I want to change to a 15-year refinancing, based on credit karma calculator, I will be paying 1,276 a month with a 2.621% APR - not sure this is correct

submitted by /u/Fame_Monster
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source https://www.reddit.com/r/RealEstate/comments/l8e5tv/need_direction_on_refinancing_my_mortgage/
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