HPLIB GUI requires python-pyqt5, but that doesn't exsit in Ubuntu 20.04

Which version of HPLIP and from which source are you trying to install?

The discussion here https://ubuntu-mate.community/t/hplip-missing-files/21782 may be of some use

HPLIB was downloaded from: https://developers.hp.com/hp-linux-imaging-and-printing/gethplip
Version is hplip-3.20.6

I had a look at the link and the bug report. It seems hplib used to depend on QT4 and now it wants QT5.
However it tries to install python-pyqt5. That package does not exist. There is python3-pyqt5.

https://bugs.launchpad.net/hplip/+bug/1876205 is marked as fixed but it apparently isn't.

$ apt show python3-pyqt5
Package: python3-pyqt5
Version: 5.14.1+dfsg-3build1
Priority: optional
Section: universe/python
Source: pyqt5
Origin: Ubuntu
Maintainer: Ubuntu Developers <email address hidden>
Original-Maintainer: Debian Python Modules Team <email address hidden>
Bugs: https://bugs.launchpad.net/ubuntu/+filebug
Installed-Size: 16.4 MB
Depends: python3 (<< 3.9), python3 (>= 3.8~), python3:any, libc6 (>= 2.14), libgcc-s1 (>= 3.0), libpython3.8 (>= 3.8.2), libqt5core5a (>= 5.12.4), libqt5dbus5 (>= 5.12.2), libqt5designer5 (>= 5.9.1), libqt5gui5 (>= 5.1.0), libqt5gui5 (>= 5.12.2) | libqt5gui5-gles (>= 5.12.2), libqt5help5 (>= 5.9.1), libqt5network5 (>= 5.12.2), libqt5printsupport5 (>= 5.10.0), libqt5test5 (>= 5.11.0~rc1), libqt5widgets5 (>= 5.12.2), libqt5xml5 (>= 5.1.0), libstdc++6 (>= 5), qtbase-abi-5-12-8, sip-py3api-12.7
Suggests: python3-pyqt5-dbg
Homepage: https://riverbankcomputing.com/software/pyqt/intro
Task: kubuntu-desktop, lubuntu-desktop, ubuntustudio-video, ubuntustudio-publishing, ubuntustudio-photography, ubuntustudio-graphics, ubuntustudio-audio, ubuntukylin-desktop
Download-Size: 2,318 kB
APT-Manual-Installed: yes
APT-Sources: http://ca.archive.ubuntu.com/ubuntu focal/universe amd64 Packages
Description: Python 3 bindings for Qt5
 PyQt5 exposes the Qt5 API to Python 3. This package contains the following
 modules:
  * QtCore
  * QtDBus
  * QtDesigner
  * QtGui
  * QtHelp
  * QtNetwork
  * QtPrintSupport
  * QtTest
  * QtWidgets
  * QtXml

If you are running Ubuntu 20.04, then you can use the version of HPLIP in the Ubuntu repositories (version 3.20.3+dfsg0-2), which has been modified to work with the Ubuntu python3 and qt5 packages.

Remove the HPLIP installation from hp.com and install the Ubuntu version with
sudo apt install hplip-gui