As VaSA said, there are the fine screwmount Takumars, and the less-desirable bayonet-mount Takumars. These latter, which may be labeled Takumar-A or Takumar-F or Takumar Bayonet, are substantially the same as their Pentax SMC counterparts, but without the special SMC coatings. They are still multi-coated, they just have less magic juice on them, and thus don't demand the same premium prices.
I have no problems with the Tak-A 70-200/4 that cost me all of US$9 shipped. That's the same lens you have there. I take mine out for a walk every now and then and it behaves just fine. Doesn't try to hump my leg or anything (ie, it's not a dog). Yours will work fine on a K5. Be sure to read-up on using manual-focus lenses (MFL's) on your camera:
https://www.pentaxforums.com/forums/pentax-beginners-corner-q/110658-using-ma...x-dslrs-f.html -- basically, set the menu to Aperture Ring Permitted, and set the lens' aperture ring to A. Have fun!