Recasting mortgage (i.e. reamortizing) vs. refinancing?

In September I bought a house for 255K. After down payment the mortgage principle is 242K, 30 year term, 5.87%. In October I sold my other property and now have 175K payment I would like to make towards my mortgage.

I want to know if I’m better off making a large lump sum payment and asking the mortgage company to reamortize with the same terms and interest rate. Or if I should actually refinance, get a new interest rate and 15 year term.

Also I was lead to believe that if I refinance, since it would be a rather small mortgage loan (@65K), that I would NOT qualify to get the most competitive rates (like 5 or 5.1%), maybe only reduce interest rate to about 5.5%. Does that sound right for those of you in the know about mortgages?

Also what is considered the break even point for paying closing costs to get the better rate/payment terms? Is it simply a matter of whether you save overall in comparison to the what the total payments would have been under the previous conditions. Or is it that you need to be in the property for a certain number of years? What is the real deal?

I’d love to hear your thoughts and advice. Thanks

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