The truth is...reds are a nightmare, but they are not limited to the K5 or to Pentax. I spent an entire day last year searching various sites like Flickr and Pbase and found that Canon and Nikon reds were also problematic, as much or even more than Pentax.
I can only tell you my experience, it may help you some. The brighter the light, the worse the reds "melt"...as in the OP photo. Decreasing exposure, shooting Raw and desaturating can also help...some.
I have also found that changing settings can help with reds...try "reversal film" it seems to get a more true to life red in the Jpeg.
Here are a few of my recent reds, most are close or very close to the true color of the birds. Keep in mind, these Cardinals are all different shades of red in real life, so they won't appear alike.
Using "reversal film" this Jpeg is very close to his true color without processing.
This was from a Raw and is close but just a shade too orange. He is an old bird and does have an orange tint, but the hue is off just a half shade. On a Canon he would look like a Florida orange!
I see this little guy up close every day, and this is very, very close to his true color. The key was in the light, it was just right and I kept the exposure down. Processed from the Raw.
Another older guy.....but this one is also very close to his true color. From the Raw, shot keeping the exposure down.
Also very close, keeping the exposure in control and processing the Raw file.
To sum it up in my experience, reds are tough, and it is work to get them right...or even close, but it is possible. I used to blame Pentax, but do your own search, you will find plenty of horrible reds from Canon and Nikon.....and many other makers too. I think it is a sensor problem that is pretty much universal.
Regards!