The fully charged voltages for the INOV8 batteries were both 8.0V, while the Pentax one was 8.35V
The former immediately dropped to about 7.5V, while the Pentax dropped to 8.0V. That is a big difference which suggests a much smaller battery (with a larger internal resistance) inside the package.
I don't know what the camera actually needs but the Pentax dropped quite rapidly at the very end from say 6.5V to 6V within 30 minutes so I regarded it as the end of its life.
I think the INOV8 batteries are either poor fakes, or there is something strange about the Pentax charger. However, since the INOV8 batteries have a slightly lower voltage, one would think that any given charger would charge them for longer!
Of course, Amazon advertise the INOV8s specifically for the K5 so in any case there is something very badly wrong.
Finding a contact email address for Amazon customer service is impossible (obviously intentional, looking at their website) and I eventually send a message using some unrelated form on their website. To their credit they responded quickly (on a Sunday!) with the mailing label.
However I also eventually found (using google!) an address for them
here:
Amazon.co.uk Legal Department, Patriot Court, 1-9 The Grove, Slough, Berks, England SL1 1QP which I have sent the test results to.
Which still leaves me with which battery to buy? Can anybody recommend a battery as good as the Pentax one?