I did the same thing earlier this year. Just be aware that after that program don’t up your mileage a fuck ton, your joints won’t be prepared. I went the route of trying to work on upping my 5k speed after the C25k plan and when I’m happy with that I’ll move towards 10k. My end goal years down the line is to run just 1 marathon in my life.

I did the UK variant of Couch to 5K (9 weeks, final goal is 30 minutes at any pace, not 5km) three years ago. I'd never run before in my life.

Instead of chasing pace after finishing that, I worked on increasing duration and distance. That was after realising that every time I'd forced myself to get faster I'd picked up some injury. Pace naturally increased as I got fitter.