To the OP, have you tried repeating the test on other outdoor subjects to see if the back focus issue remains consistently out? If it is reset the K-5 to the default setting and try again before resetting any fine AF adjustments.
If still a problem after that try the lens on a different camera body and see what happens. After that you should know where the problem lies.
I suspect it might be a case of you not being able to blame Pentax for Sigma making a duff lens and you've just been unlucky to get that one but you'll need to confirm that with some further tests.
My own experience with some Sigma lenses that they can struggle to obtain spot on focus (they just start hunting back and forwards in low light and can stop anywhere often way off!)

Focus shift !
https://photographylife.com/what-is-focus-shift
Also as you say the effect of different lighting / colour temperature.

They're really good!
I see #6 as a world map.
#2 as a single flying bird with a long neck (swan perhaps?)
#4 as a perched blackcap.
#5 as a single flying bird representation
#7 as the Loch Ness monster

I believe that if the lens isn't identified the only option given is 'apply all', or at least that's what the K-5 manual states.
It is said that Sigma reverse engineer the electronics for the Pentax mount so many of them report incorrectly in the Exif.
The lens sends a code to the camera and it is this that isn't being recognised. Do you have the latest K-5 firmware - if not updating it might sort it out. The last version was v1.16 http://www.ricoh-imaging.co.jp/english/support/digital/k-5_s.html

[edit: with the info found below it won't help but still worth updating if not current.)

For info that Sigma lens IS being identified as: Sigma 18-200mm F3.5-6.3 DC or Sigma DL-II 35-80mm F4-5.6 or Sigma DF EX Aspherical 28-70mm F2.8 or Sigma 70-300mm F4-5.6 Macro or Sigma 55-200mm F4-5.6 DC, Sigma used the same code for all of them so Pentax may ignore that code simply identifying it as a 'Sigma lens' which is the best they could do in the circumstances.

If the lens focussing is out ask Sigma to service it for you.

The problem is almost certainly that your zoom is seen by the camera simply as Sigma lens so the camera is unable to store focus adjustment details for it. The camera doesn't recognise the lens! Generally third party lenses aren't supported apart from some where the lenses are the same as Pentax ones but rebadged.
Your other lens is a smc PENTAX-FA 50mm F1.4 so the camera recognizes the lens and it works for that.
Even if a zoom lens was recognised there is often some focus shift throughout the zoom range in them so it might not be possible to get it 100%.
What Sigma lens is it? (Presuming that has been reported to the camera accurately as some third party lenses fail even to do that!)

An M42 mount DSLR perhaps then! (Or even M37.)


The image is viewed on what was the reflex screen!

Actually what would be good is a smaller, lighter FF DSLR akin to an ME/MX. Something suggests to me that could only be achieved in something similar to the current FF Sony offering (mirrorless.) Perhaps buying in a rebadged/adapted design.

On eBay some things go for well under their normal value and others much more. It all depends on what someone is prepared to pay and how many are after it at the time of the sale. A bit of a lottery really!

Agreed on that. Yes, they're fine some of the time but one doesn't wish it to get confused by something out of the ordinary. Same with that photo of a lifetime opportunity.

It's nothing new. Many consumer level DSLRs have an auto scene mode setting (including some Pentaxs.) But it's really preferable to understand the camera settings and know what you're doing.

I write jpegs and raw to BOTH cards without issue. But I don't normally use rapid fire modes.