Question Should I get a new motherboard or CPU?

[othefourth]

I'm having an issue in some games that are more graphically taxing (battlefield 5, GTA, etc.), where no matter what quality setting every 30 seconds or so I drop to 15 or less fps. Playing battlefield 5 on ultra graphics settings is beautiful and I'm getting about 90 fps I just wish it would stay like that. According to pcpartpicker.com my motherboard and cpu aren't compatible, though I've been using them for a while together and until I got my new graphics card this hasnt been an issue. I don't think it is a graphics card issue because the problem persists no matter the resolution, graphics setting, or driver I'm using. So, in the case that the issue is because of my motherboard/CPU clashing, which of the two should I upgrade?

System Summery:

Motherboard: MSI 760GM-P23 (FX) Micro ATX AM3+

GPU: MSI Nvidia Geforce GTX 1660 ti 6GB Ventus XS OC

CPU: AMD FX-8350 4 GHz 8-Core Processor

Physical Memory: Corsair Vengeance 16 GB (2 x 8 GB) DDR3-1600 Memory

I'm not great with computers so I don't know if theres anything else I need to provide. Please let me know if I forgot something crucial to add!

Edit:
Thank you all for the help! In the process of trying to find a good cpu upgrade i'm finding more and more compatibility and outdated technology issues. It looks like I'm going to have to replace the CPU, because it is old, the motherboard, because it is old as well and a "new" cpu that works with it won't have the quality I need. I also will need to get new DDR4 RAM which is a big bummer because I just got these new sticks for Xmas ¯\(ツ)/¯ .
Here's what I'm looking at; Again thank you for all your help and if I'm able to ask for any more of your time please tell me what you think of this build.

Motherboard: MSI B450 TOMAHAWK ATX AM4 Motherboard
GPU: The same 1660 ti
CPU: AMD Ryzen 5 2600X 3.6 GHz 6-Core Processor
RAM: Corsair Vengeance LPX 16 GB (2 x 8 GB) DDR4-3000 Memory

 

[othefourth]

The X variants have a better cooler and slightly higher clock speeds but if you where to go aftermarket on the 2600/3600 you could probably get pretty close to the X variants in performance.

Last question, is there any issue with a B450 MB Tomahawk Max, 2600X, and 2x8gb 3600mhz of RAM? I really appreciate the help by the way this day has been very educating!

 

[86zx]

Last question, is there any issue with a B450 MB Tomahawk Max, 2600X, and 2x8gb 3600mhz of RAM? I really appreciate the help by the way this day has been very educating!

All looks like it checks out! You might even be able to use the same cpu cooler I was able to use a wraith cooler on a fm2 socket

 

[WildCard999]

Last question, is there any issue with a B450 MB Tomahawk Max, 2600X, and 2x8gb 3600mhz of RAM? I really appreciate the help by the way this day has been very educating!

There shouldn't be any issues, just make sure the memory is in the correct slots and XMP is enabled to get the memory to run at the correct speed, voltage & timings as speed makes a big difference in gaming for Ryzen.