It doesn't matter whether you have a graphics card on the mainboard or not. I work with both, i.e. with an integrated GPU in the CPU chip and an external graphics card on the PCIe slot. As far as I know, you can only control one of the two cards with 1 monitor.
The fact is, the Ryzen 5 5600X does not have an integrated GPU, i.e. graphics. Therefore, an external graphics card is required, which is then plugged into the PCIe slot of the mainboard. The clear answer to your question: NO - a Ryzen 5 5600X will not run without a dedicated graphics card on the board. You have to have some kind of graphics.
You can also find out directly on the AMD website whether a CPU has an integrated graphics unit or not, e.g. for this processor here
https://www.amd.com/en...An internal graphics unit on the CPU die is usually not very powerful, so it is hardly suitable for demanding games.
Regards
Big Tom (;-)