Have you considered utilizing a tool like Webinar Jam? You can pre-record your webinars, turn them into evergreen webinars and set the entire system up to provide specific dates and times for the recording, including a, "Your in luck, our next one starts in 15 minutes!" option or something like it.

Three weeks is a long time to wait when we are a society that want instant gratification so offering something like this may be a key for more frequency.

Also, if you have a way to monitor the open rate of those five reminders, I'd encourage you to look at that statistic. Even though your current schedule is three weeks out, five reminders seem a little high and I'm thinking you'll see that the two out of the five e-mails don't even get looked at.

Other suggestions would be to look closely at your webinar title, the length of the webinar and even the hook you are pitching to encourage people to watch. You want to give off a high perceived value to entice registration and attendance.