Five minutes is an incredibly long time to wait at a roundabout or a junction. It probably wasn't longer than a minute, maybe two at most. The nature of roundabouts is that gaps do appear even during busy times, and normally relatively quickly. Turning right out of a junction can be more problematic because the traffic in each direction doesn't correlate so can prevent gaps from appearing. But as I say, that's not how it works at roundabouts because the flow of traffic creates gaps naturally.
The fact is that you cannot go unless it is safe. I disagree entirely that sometimes you need to 'take a chance'. You can see the gaps and you know how quickly you can accelerate away. As you gain more experience at driving you will become more competent at spotting gaps, and should be able to pull away quicker. So it's about being able to spot the gaps that you can safely take. If you find yourself just not being able to spot a gap you can take for a prolonged period, you just have to wait. Over time and the more you drive, the less of a problem that will be.