Chainset / cassette query?

I have a 2012 specialized allez 16. The bike came with the shimano 2300 groupset. While I love the frame the groupset is cheap and problematic. I want to upgrade to shimano 105, but am somewhat confused as to what chainset / cassette combination to go for. The allez has 39/59 rings and a 13/26 cassette. I'm really disappointed with the lack of speed I can achieve in the highest gear and the lowest could do with being a bit lower for tougher climbs. I've been looking at a 105 standard 39/53 and 11/28 combination.
Is this a viable combination, or will the difference in gearing be too great?
Is this a viable combination, or will the difference in gearing be too great?
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