Ok guys, I'm back!
Two weeks ago I sent my Pentax K5 with Sigma 10-20 F4-5.6 to the Sigma authorized repair distributor in my country.
A few days later I received the diagnosis: "The lens had the latest version of the software. Lack of communication with the Pentax K5 is caused by a break in the ground circuit of the camera bayonet and a twisted bayonet. In fact, 1.5 years ago the camera mounted to the tripod fell on the ground and the bayonet was pull out of the body, but I fixed it and everything worked as before.
They asked for 80 USD, which was the 40% of the amount I paid for the lens. I refused because it was too much for an old lens in my opinion which still works, but not with my K5. I started thinking about buying a new body such as K3 II/ KP... or even Sony A6300
but I decided to wait.
And now the best part! Last week I got my camera back. Out of curiosity, I have attached the Sigma 10-20 to the K5, turn on the camera and ... AF worked. I couldn't believe so I unmounted the lens, mounted it again, turned it on and it showed me AF.C again. I changed the modes, did couple of test shots and it worked as my other lenses. Each time the camera recognizes the lens and AF works. I have no idea what happend.
My total cost of this repair was less than 4 USD - shipping cost.
Thanks to all for your help!
Cheers,
Maciek