How do I reset my imac 5.1 tiger to factory settings WITHOUT a disk

To factory reset an iMac without a login or keyboard, you can try the following steps:

1. Boot the iMac in Target Disk Mode: Connect the iMac to another Mac using a Thunderbolt cable. Power on the iMac while holding down the T key. The iMac should appear as an external disk on the other Mac.
2. Reinstall macOS: Open the Disk Utility app on the other Mac and select the iMac disk. Choose "Erase" and follow the on-screen instructions to erase the iMac's drive. After erasing, quit Disk Utility and follow the on-screen instructions to reinstall macOS.
3. Restore from Time Machine Backup: If you have a Time Machine backup of the iMac, you can restore the backup to the iMac after reinstalling macOS.

If these steps don't work, you may need to seek assistance from an Apple Store or a professional repair service.

insert installation disk to re-install factory settings

You can restore your computer to the factory state, without any of your data, but this will require (at a minimum) the install disk(s) that came with your system, (prior to OSX 10.7) Systems built for 10.7 and later may not have shipped with disks, but Apple will happily provide you those disks at little to no cost.

You may download an ISO image from the internet. The higher system supported by the G3 processor is MacOS X 10.4 "Tiger".

dont put in disc (system settings > date and time)

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iMac Technical Support Number 1 833 493 0111 iMac Help

Hi, You need a Tiger or Leopard installation disk. Then You start up the system holding down "C" instead of installing you start the "disk utillity" and repair it.
You can access singel user mode by starting up the system holding down command + S.
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That Mac will run 10.4 Tiger, but I would recommend 10.3 Panther. You can download all updates through sofware update after the install is complete. You should be able to find installer disks on eBay for cheap.

The disk utility program is the key. You need to run the app to repair disk permissions. You may have to start up from the installer disk for Tiger to get access to the program.