How can I create delays between failed Queued Job attempts in Laravel?

What you can do is something like this:

// app/Jobs/ExampleJob.php
namespace App\Jobs;

class ExampleJob extends Job
{
    use \Illuminate\Queue\InteractsWithQueue;

    public function handle()
    {
        try {
            // Do stuff that might fail
        } catch(AnException $e) {
            // Example where you might want to retry

            if ($this->attempts() < 3) {
                $delayInSeconds = 5 * 60;
                $this->release($delayInSeconds);
            }
        } catch(AnotherException $e) {
            // Example where you don't want to retry
            $this->delete();
        }
    }
}

Please note that you do not have to do this with exceptions, you can also just check the result from your actions and decide from there.

You could manually release the job using the Illuminate\Queue\InteractsWithQueue method

$this->release(10);

The argument will define the amount of seconds until the job is available again.

Check the section Manually Releasing Jobs in the official documentation for version 5.1.

Laravel 8

/**
 * The number of seconds to wait before retrying the job.
 *
 * @var int
 */
public $backoff = 3;