I'd love to know the rationale behind it. Especially when it goes from '10 mins run: 3 mins walk:10 mins run' straight to 25 mins run. If you can run for 10 mins, no way do you need a 3 minute run. And the jump from 10 mins straight, to 25 mins straight is huge.
Personally (and I'm only a physio who runs, and has a qualification you cannot possibly check!) I would gradually increase your run time and decrease your walk time - always aiming to run until you cannot run any further, and then only walk until you are able to run again.
Then once you can run for 30 mins without stopping, look at picking up the pace.
Simultaneously, I would be doing HIIT training to increase cardiovascular fitness - and this can also be running. So for example a flat out run as fast as possible until you cannot run any more, then a short rest or jog, then flat out again. But this probs needs a GP approval if you are unfit or have other health issues.
As it stands, the couch to 5k looks about as well-researched as those ludicrous 'squat challenges' you get on facebook, where you imagine you will go from 10 squats to 140 squats (or whatever) in a month.
I'm not saying don't do it, but if it doesn't work out, don't blame yourself - maybe look at a different way of training.
and yes, jogging is slow running.