The J-5 was the first jet fighter China actually started to produce. That would be the MiG-17. Prior to that, MiG-15s had all been imported, but none domestically produced.
The first jet fighter ever imported to China and wore the PLAAF insignia was the MiG-9. That was based on a secret project Messerschmitt concocted in the closing days of World War II. A few of these aircraft are still in some museums in China.