32-bit version of Crysis crashes on all modern AMD processors. For older Bulldozer-based processors (this includes AMD FX) there is a fix. It's a .bat file which starts Crysis with changed affinity. You can find content of the file here on forum or on the Internet. For the latest Ryzen processors there is no known fix, so using 64-bit version is the only way how to play Crysis on these systems for now.
The fix should work for you if you have AMD A4-5300 (see below for how-to), but as Aigami said, there's nothing wrong with using 64-bit version. It is somewhat more prone to random rare crashes but it works well.
If you really want to use 32-bit version of Crysis:
1) open notepad and copy&paste the following code there
start "" /affinity FE "Bin32\\Crysis.exe" -mod sfwcl
2) save it as amd_fx.bat (no .txt suffix) to Crysis directory (e.g. "C:\\Program Files\\Electronic Arts\\Crysis")
3) double click on the new file and 32-bit Crysis should start