I think it's perfectly within reason to replace the needed drivetrain parts. That shouldn't cost too much, probably well south of a hundred bucks.
I think for the price of a full upgrade with brand new 105 5800 and wheels, I'd be looking pretty closely at taking the extra step to a complete new bike instead.
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Genesis 49:16-17
"Well, well!" said Holmes, impatiently. "A good cyclist does not need a high road. The moor is intersected with paths and the moon is at the full."