Now running 5k, advice on next goal please

I would generally advocate going longer when you're only at 5K. The training for 10K will improve your pace somewhat.

If you're not race training then a 10K session is quite good. It only take an hour or so, and it's long enough to feel worthwhile.

The 5K distance is kind of a decision point. There is no single path to what you do next; it mostly depends on what you want out of running. You may not yet know what you ultimately want, so you should try different things to see what you like.

I built from 5K to the 5 mile distance, entered a 5K race, and came away not terribly convinced that I wanted to deal with the administrative and logistical stuff that surrounds entering races. But a lot of people told me races were fun, so I entered a 10K. Then my sister told me, "You know, a 10K is almost half of a half marathon." It took me a while to parse that statement. That pushed me into my first half marathon, which ultimately led me to run marathons.

But marathons aren't for everyone. Some people don't want to run any races longer than 5K. I met a guy at a 5K who runs one every weekend and just isn't interested in longer distances. Some people regard 5K as too short to be worth messing with. I'm not quite in that camp; I need a reason other than, "Hey, there's a race!" to run a 5K. Some people don't want to race at all, they just want to run socially or for stress relief and pleasure. Some people only run to burn calories; the ones who don't find a more compelling reason tend to stop running when life gets in the way.

For where you are now, I'd recommend stretching the distance until you find your comfort zone for recreational running. I'd also recommend entering a race or two just to experience the environment, meet people in the running community, and see whether you like that type of experience. You might be surprised; I was. There are also races that are more events than time competitions, with themes like obstacles in the way or colors splattering the runner. And there is trail running, and cross country running, and track running. Each of these has its own character, and some people find that they're attracted to one or more of the less standard types of running.

I hope you find the form of running that really speaks to you, and that you have a lot of fun in the process of finding it.

I'd say increase distance. At least to 10K range. The ability to use running as a means of exploration and adventure is by far the best thing about running.