The best replacement for 5800k is 6800k.

The best alternatives to 5800k are rated as following:
★★★★★  6800k
★★★★  fx 6300
★★★★  7850k
★★★★  6790k
★★★  6600k
★★★  760k
★★★  5600k
★★★  6500k
★★  7700k
★★  3220
★★  fx-6300
★★  a10 6800k
★★  fx 6100
★  i3 4130
★  i3 3220
★  a8 5600k
★  fx 4300
★  a10 5700
★  a8-6600k
  5700
  a10-6800k
  3870k
  amd fx 6300
  a8 5600

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Speaking about 5800k, one probably shouldn't forget about 6670.

Other search terms related to 5800k and their ratings are:
★★★★★ 6670
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5800k
6800k
fx 6300