In reply to MonkeyPuzzle:
>Should I start pushing distance straightaway, or is it best to get established at 5k for a little bit first (I'm thinking like climbing grades so could be completely different)?
I think only you can answer that, depending on how you feel afterwards. It could be that you ache like you've been fighting a dozen ninjas, or it could be you feel refreshed and ready to go some more.
It might be better to focus on locations, rather than distance. You mention linked parks, so set one of them as your target. Once you can get there and back, try and explore it a bit. Then add the next one. I find it more interesting to check out interesting things on the map, rather than to think, 'right I need to get in +20k.'
Remember, if you're new to this running lark, there's a wonderful world of injuries to explore as well. Go by how you feel. Just because you did 5k yesterday, it doesn't mean you have to do 6k today. Some cross training is always a good idea.