Unable to use pip 20.3.4 with Python3.5.2 on Anaconda 4.11.0, Windows 10

Question

I would like to use python 3.5.2 in my conda environment. It was installed from conda-forge channel by running

conda install python=3.5.2 --channel conda-forge

pip 20.3.4 came together with it.

My problem is that pip install does not work. For instance pip install notebook returns only warning

DEPRECATION: Python 3.5 reached the end of its life on September 13th, 2020. Please upgrade your Python as Python 3.5 is no longer maintained. pip 21.0 will drop support for Python 3.5 in January 2021. pip 21.0 will remove support for this functionality.

The notebook is not being installed.

pip install notebook --verbose returns

Using pip 20.3.4 from C:\Users\User\anaconda3\envs\gcp\lib\site-packages\pip (python 3.5)
Non-user install because site-packages writeable
Created temporary directory: C:\Users\USER\AppData\Local\Temp\pip-ephem-wheel-cache-j9zyeti6
Created temporary directory: C:\Users\USER\AppData\Local\Temp\pip-req-tracker-wfscnb24
Initialized build tracking at C:\Users\USER\AppData\Local\Temp\pip-req-tracker-wfscnb24
Created build tracker: C:\Users\USER\AppData\Local\Temp\pip-req-tracker-wfscnb24
Entered build tracker: C:\Users\USER\AppData\Local\Temp\pip-req-tracker-wfscnb24
Created temporary directory: C:\Users\USER\AppData\Local\Temp\pip-install-4drsvs_d
1 location(s) to search for versions of notebook:
* https://pypi.org/simple/notebook/
Fetching project page and analyzing links: https://pypi.org/simple/notebook/
Getting page https://pypi.org/simple/notebook/
Found index url https://pypi.org/simple
Looking up "https://pypi.org/simple/notebook/" in the cache
Request header has "max_age" as 0, cache bypassed
Starting new HTTPS connection (1): pypi.org:443

Can someone help me to tackle this issue? I run in on Windows 10 with Anaconda 4.11.0