What used to be the i7 was (like with the i7-7700) now occupied by the i9 line
The value price of the 12600k is just much better
Looking up the numbers instead of reading them like tarot cards, I can tell you that the i7 7700 is a 8 core processor with a max turbo frequency of 4.20 GHz, and the i5 13600 is a 14 core with 6 cores that can do 5 GHz, and 8 efficiency cores capped at 3.7GHz. And both support VT-d, which is about the only feature I would care about :D
Breaking both down we have 3 things to take note of:
i5/i7 - indicates relative performance or feature set within a given generation, bigger is generally better
13/7 - the generation of processor
600/700 - where Intel rates a given processor within a generation, this is consistent and doesn’t (to my knowledge) involve overlap between i3/5/7/9 - generally bigger is better.
So i5-13600 is a thirteenth gen i5, type 600. i7-7700 is a seventh gen i7, type 700
Then you get the legion of letter suffixes determining other features, mobile SKUs etc.
In general, you can only infer very little from the marketing names. To have any actual idea, you have to look at benchmarks. In practice, 13600 is ~70% faster per thread, and has 2.5 times the threads.
i5-13600k is around 38000 points (https://www.cpubenchmark.net/cpu.php?cpu=Intel+Core+i5-13600...)
i7-7700k is around 9600 points (https://www.cpubenchmark.net/cpu.php?cpu=Intel+Core+i7-7700K...)
So the new i5 is nearly 4x faster than the old i7. New CPUs have come a long way over the last few years.