Is there a wireless charger I can use for my iPad 5th gen?

With good light, extreme care and a wooden or plastic toothpick, you might carefully try to dislodge any foreign material that may have accumulated in the charging port.

Otherwise, entrusting this to a technician at the Genius Bar of your local Apple Store or Apple Authorised Service Provider might be your best option.

Genius Bar Reservation and Apple Support Options - Apple

It doesn't charge wirelessly.

See the following instructions: If your iPad won't charge - Apple Support

iPad fundamentally does not support wireless/inductive charging. This capability cannot be retrofitted. Consider that wireless charging is also significantly less efficient than a direct (wired) connection to the Power Adapter.

iPhone models that support wireless charging have glass back-panels and internal inductive charging loops - all of which are missing from iPad.