As of my current knowledge and research, here are the top 5 gaming phones available in the United States under $500

Realme GT Neo –

 The Realme GT Neo is a mid-range gaming phone with a 6.43-inch Super AMOLED display with a 120Hz refresh rate. It is powered by a MediaTek Dimensity 1200 chipset, which provides excellent gaming performance, and comes with up to 8GB of RAM and 128GB of storage. The phone has a triple-camera setup at the back, with a 64MP primary sensor, and a 16MP selfie camera. It is powered by a 4500mAh battery with 50W fast charging support.

Realme GT Neo

POCO X4 Pro –

The POCO X4 Pro is a budget-friendly gaming phone with a 6.67-inch IPS LCD display with a 120Hz refresh rate. It is powered by a Qualcomm Snapdragon 870 chipset, which provides excellent gaming performance, and comes with up to 8GB of RAM and 256GB of storage. The phone has a quad-camera setup at the back, with a 64MP primary sensor, and a 20MP selfie camera. It is powered by a 5160mAh battery with 33W fast charging support.

POCO X4 Pro

Samsung Galaxy A52s 5G –

The Samsung Galaxy A52s 5G is a mid-range phone with a 6.5-inch Super AMOLED display with a 120Hz refresh rate. It is powered by a Qualcomm Snapdragon 778G chipset, which provides good gaming performance, and comes with up to 8GB of RAM and 256GB of storage. The phone has a quad-camera setup at the back, with a 64MP primary sensor, and a 32MP selfie camera. It is powered by a 4500mAh battery with 25W fast charging support.

Samsung Galaxy A52s 5G –

Xiaomi Poco F4 –

The Xiaomi Poco F4 is a mid-range gaming phone with a 6.67-inch IPS LCD display with a 120Hz refresh rate. It is powered by a Qualcomm Snapdragon 888 chipset, which provides excellent gaming performance, and comes with up to 12GB of RAM and 256GB of storage. The phone has a triple-camera setup at the back, with a 108MP primary sensor, and a 20MP selfie camera. It is powered by a 5000mAh battery with 67W fast charging support.

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Xiaomi Poco F4

OnePlus Nord 2 5G –

The OnePlus Nord 2 5G is a mid-range phone with a 6.43-inch Fluid AMOLED display with a 90Hz refresh rate. It is powered by a MediaTek Dimensity 1200 chipset, which provides good gaming performance, and comes with up to 12GB of RAM and 256GB of storage. The phone has a triple-camera setup at the back, with a 50MP primary sensor, and a 32MP selfie camera. It is powered by a 4500mAh battery with 65W fast charging support.

Xiaomi Poco F4

Please note that prices and availability may vary over time, and newer models may have been released, and there may be other options worth considering as well.