Brother MFC-J5320DW won't install on Tahoe

when ever one updates to a new macOS version one has to be prepared for the possibility that

the maker of your printer (and other hardware really) need to update their driver before it will continue to work

Downloads | MFC-J5320DW | Others | Brother

brother only officially support macOS Monterey (version 12) for that model

it's costly for them to keep making new drivers for models they may not sell anymore so some, stop sooner rather than later

but it support airprint (a generic printing interface apple made) according to their documentation MFC-J5320DW.ashx

try Print using AirPrint - macOS Computer, iPad, iPhone, iPod touch

more

MFC-J5320DW setup airprint - Google-

you can check Gutenprint Supported Printers if they support your driver

As Rudegar mentioned, the Brother MFC-J5320DW has AirPrint support.

See also About AirPrint - Apple Support.

If nothing else works, you may want to try a full power-cycle sequence (do not forget the Wi-Fi router):

• Power off the router, the printer, the MacBook Pro, the iPad, and all other devices/computers connected to the same network.
• Wait two to three minutes.
• Power on the router.
• Wait a minute or two.
• Power on the printer.
• Wait a minute or two.
• Power on the MacBook Pro, the iPad, and all other devices/computers.

AirPrint works with wireless (Wi-Fi) or wired (Ethernet) network connections. This means that, if necessary, you could wire the printer by Ethernet cable to one of the LAN ports of the Wi-Fi router (instead of wirelessly connecting the printer).

You're welcome! Glad to hear that it is working.