The Ryzen 5500 box processor comes with a Wraith Stealth cooler, which is a very minimalistic heatsink and fan. However it should be adequate to keep temperatures lower than what you are experiencing. It would have come with thermal paste pre-applied, make sure the four screws are securely tightened all the way in, and that none are cross-threaded.
Also check the motherboard BIOS (or software utility) for the CPU fan curve setting. If it is set to silent change this to normal (default) setting. Verify the fan RPM speed increases with temperature. It should be reaching 100% well before hitting 90°C.
Ryzen R7 5700X | B550 Gaming X | 2x16GB G.Skill 3600 | Radeon RX 7900XT
Ryzen R7 5700G | B550 Gaming X | 2x8GB G.Skill 4000 | Radeon Vega 8 IGP
Ryzen R5 5600 | B550 Gaming Edge | 4x8GB G.Skill 3600 | Radeon RX 6800XT