Not necessarily.

Say you bought it in 2015 for $325k with $25k down.

Starting out, you'd have $25k of equity -- You have a $325k house and owe $300k on it. You're 7% of the way to owning your house. The bank owns the other 93%.

After 5 years, let's say you owe $280k. So now you have $45k equity. You own 14% of the house.

So now you want to refinance. There are a few ways you could refinance. You owe $280k right now. You could take out a new $280k mortgage at a better interest rate to save money. This wouldn't impact your equity, and nothing has been "lost". You still owe $280k on a $325k house. You still have 14% ownership. Alternatively, you could also choose to give up some of your ownership in exchange for more money. If you take out a $325k mortgage while refinancing (they wouldn't let you do this), you now have no equity -- you owe $325k on a $325k house.