I'm in the process of refi'ing from a 30 year fixed at 5.75% at USAA to a 15 year fixed at 4.625% at PenFed. For me I didn't even really have to run the math very hard because I knew it was a great deal for me. Over the next 15 years I'll be saving $22,000, and I'll then get an additional 14 years of no mortgage payment, which is worth another six figures to me. My closing costs will be (I think) under $1,000.
Based on the numbers you gave, you're not going to hit break even on your refi for a very long time, so you're basically paying your closing costs in order to extend the fixed period on your payments. If I were in your shoes, I'd only do that if I knew for certain that I'd be in the house at least another 6-7 years, maybe longer, depending on the particulars of your current loan and what rates it might go to when it resets, as well as what the closing costs on the new loan will be. Also, if your current mortgage payment is a challenge for you to afford, you might need to refi just to avoid the risk of getting into an unaffordable payment situation when your current loan resets.
"At times the world can seem an unfriendly and sinister place, but believe us when we say there is much more good in it than bad. All you have to do is look hard enough, and what might seem to be a series of unfortunate events, may in fact be the first steps of a journey." Violet Baudelaire.