Tokyo in October

Be aware October is in typhoon season, so if you plan hiking or rural activities, keep track of the weather forecast. A trip I took to Japan pre pandemic was interrupted by an October typhoon, I had to alter my plans on the fly to avoid the most heavily hit and flooded area of the country, trains were disrupted, etc.

5 days is a bit tight time-wise.

I highly recommend checking out two areas in the Japanese Alps. You should be able to see foliage at high altitudes.

Kamikochi (breathtaking national park with good hiking) -Takayama (old town)-Shirakawago (quaint village) - Kanazawa - (bonus destination) Tateyama Kurobe (series of cable cars, ropeways, with hiking if time allows)
https://www.japan-guide.com/e/e6040.html
https://www.japan-guide.com/e/e5950.html
https://www.japan-guide.com/e/e5900.html
https://www.japan-guide.com/e/e2167.html

Nakasendo: Tsumago, Magome, ... village towns along an ancient transit route.
https://www.japan-guide.com/ad/nakasendo/

For a mountain experience visit beautiful Takayama,

You have been given some great ideas!

This foliage map should help you make decisions:
https://www.japan-guide.com/e/e2014.html

If you go to Nikko, you will see foliage. It's a bit far from Tokyo and I suggest you stay at an onsen ryokan/hotel for one night for the ultimate Japanese experience.

Don't forget to check my recent trip report. I was in Japan for the cherry blossom season in Mar 2023.