First of all I'm also a KGS 5k, and I'm not talking about your moves but that of your opponent, however you did lose the corners but not really the center since you killed of a big group near it
A game like this makes me wonder how Black made it to 5k, everyone should learn why the 3-3 point invasion at the beginning is usually bad (if you follow a strategy it's ok). But Black even tenukis after 10, this is a mistake (not that I think that the invasion is good) and Black even makes the same mistake in the LR corner, below I explain what I mean.
After that Black created one weak group after another with moves like:
and 
, you used these overplays by splitting and attacking him and turned it into a big fight, that you did win. That was well done, I don't think I could have done that 
Here a bit about the "bad" plays in the corner by Black. Maybe you already know this, but beginners might want to know this.
Normally the joseki is something like this: (sorry I reversed the colors in the diagramms)
This is normal but it is better for Black, because Black's wall (influence) is more worth then White's territory which is about 10 points.
But if White tenukis after 6, Black can press White down.
I believe 4 is needed to live, so Black has sente to answer White's move or play an extension somewhere around "a".
White's teritorry is even smaller now and he didn't really gain much from playing elsewhere.
Overall black took the corners because he plays for territory, but then he throws away his strategy to attack you after he made you strong, a very strange play. If he waned to attack you or didn't like your influence , he should not have taken the corners in the first place.
I say that the 3-3 invasion in the fuseki is bad, but that's my opinion.
If what anything I said above is wrong, then please correct me! I'm not a strong player and always happy to learn more
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