Don't remove the default Python 3.x version because removing it can break a lot of things like the terminal, the Software app and many other apps. For more information see this question: Removed Python 3 and now Ubuntu Software Center, terminal and other applications don't work. The good news is that even if you break those things it is possible to restore the original Python 3.x version by booting Ubuntu into recovery mode, and then Ubuntu will work normally again.
Instead of replacing the default Python 3.x version entirely the recommended way of installing another Python 3.x version is to keep the existing Python 3 and install the new Python 3 version alongside it. Then you can use a program called update-alternatives to select which one of the Python versions you want to use.
Add Python 3.8 to update-alternatives so that you can switch between Python 3.5 and Python 3.8 by running update-alternatives --config python3.
sudo update-alternatives --install /usr/bin/python3 python3 /usr/bin/python3.5
sudo update-alternatives --install /usr/bin/python3 python3 /usr/bin/python3.8
update-alternatives --config python3
After you are done using Python 3.8 you can switch the it back to the default Python 3.5 version.
List installed versions of Python: update-alternatives --list python
Switch between Python versions: update-alternatives --config python
From the terminal command-line Press <enter> to keep the current choice[*], or type selection number:
