If it makes you worry, see the specialist, do the tests. 10km/hour is a pace of 6:00/km. This is hardly jogging (I use a different definition of jogging but I see it as more skipping moving slowly forward than running). I'd say your pace is easy to (depends on your conditioning) medium effort run.
That said, you should verify whether this is accurate reading (often higher HR is a result of higher cadence which produces 'noise' that the wrist sensor isn't able to filter out). Ignore what is peak or cardio. It's irrelevant and very individual (mostly driven by your genetics). I'm 40 and my max HR is 189/190 (and RHR is 38). Most of my runs get my heart pumping harder but I don't feel tired either. My heart may be pumping 170 and I can still talk normally. Genetics. Also, assuming the readings are accurate, your Lactate Threshold may be higher (mine is 173bpm). It means, when keeping your HR below you are able to run building fatigue slower (endurance effort). With more running, adding more variety to training your heart rate may drop but this isn't really a rule. I know runners who run with a pace nearly 4:00/km and their HR barely gets over 150 and others who for the same pace reach much higher hitting 180 (I'm among them). This is a very individual thing. On one of my recent runs (nearly 2hrs long, pace: 5:08/min, lots of climbs which even more elevates HR), I averaged HR of 170bpm. I stayed 1hr over my threshold (173+) and 35min in the range 163-172bpm. Why so high? Because I can. Mind, I had clinical tests done (my wife had similar worries about my heart so I decided to check myself). The specialists said everything was fine, it's just genetics.
1) don't worry in advance.
2) if you have doubts - see the specialist, better safe than sorry.
3) verify data. I suggest investing in a good chest strap for accuracy. I never track my runs using a wrist sensor.
4) enjoy running 🙂
