Reading the specs on your HP EliteDesk 705 G5 SFF I can see why all the AMD processors are APUs (Processors with Integrated Graphics).
The PC has a extremely weak 180 Watt PSU. This PSU is adequate enough only for running Integrated Graphics. If you install a regular CPU without graphics you will need to upgrade the PSU to one at least rated between 600-850 Watts Metal rated depending on the GPU card you select.
Also you can't just install any type of AM4 processor. You need to find out if your HP BIOS version will support other CPUs that are not listed and are not 'Pro' version.
Unfortunately, AMD "Pro" CPU Versions are all OEM/TRAY. Which means it isn't normally sold in Retail stores. You would need to probably purchase the processor from HP directly or from a Foreign Retailer.
You can update the BIOS and CHIPSET through HP Support Driver Download page from here: https://support.hp.com/us-en/drivers/selfservice/hp-elitedesk-705-g5-small-form-factor-pc/27015959
If I were you before purchasing a processor open a HP Support ticket and ask them if Non-Pro AMD Processors are supported by the latest BIOS Version.
Also you will probably need to find a Low Profile GPU card to be able to install it if the Computer case is a Small case.
Also ask if you can install a regular 3rd Party PSU in that computer. Some PC Makers use OEM Motherboards that requires a special PSU cables to be able to connect and power it up.