@chibae, you are not the only one who wants a lens that is long (>300mm), relatively lightweight, fast-ish, and cheap, that produces very good image quality. They don't exist. You have to compromise on at least one criterion.
The 55-300 with TC means giving up on speed. With a 1.4x TC the widest aperture is f8. And since the lens wants stopping down, you would generally be aiming for f10-f11. That requires good light and/or slow shutter speeds and/or high ISOs. But as @csa's images show, it's better than the numbers suggest.
The various 300mm primes + TC will generally give better IQ and more speed (f5.6-f6.3, and several will work well wide open). The pick of them, in my view, would be the F*300 f4.5, FA*300 f4.5 or DA*300 f4, and maybe the Sigma 300mm f4 Tele Macro. These are all auto-exposure and auto-aperture. The lightest of them is the F*300 at about 850g. It's relatively expensive (about $US700) and hard to find but a really stellar lens.
Even the manual focus, manual aperture lenses like those @LowellGoudge suggests are still fairly hefty and they aren't dirt cheap (e.g. about $250 for the K 300 or about $400 for the M 300 f4), especially when you add the fairly-expensive and hard-to-find 1.7x TC (which adds a measure of AF). They have longer minimum focus distances (4m) and more purple fringing and CA than the later versions. But if you can live with those limitations and manual everything, the M 300 in particular is renowned for its sharpness.
If you look at 400mm primes, they are mostly heavier (1200g+) and more expensive than the 300mm equivalents. The Tokina ATX is a bit lighter, although reviews are a little mixed. I have the Sigma 400 f5.6 tele macro (77mm filter size) and it's a fine lens, but it is very hard to find and not cheap (in Pentax mount). It weighs about 1.3kg, which I find I can use handheld.
Next up are the various xx-400 zooms, like the Sigma 135-400 and 120-400, and the Tokina 80-400. They weigh upwards of 1.3kg. The Sigma 120-400 might be the pick of those.
Then there are the various xx-500 zooms like the Sigma 170-500, 150-500 and 50-500. The 170-500 is much lighter than the others at about 1.3kg v about 2kg, but I had one and it isn't as good or as reliable as the 400mm prime. I think a 300mm + TC would be a better option.
Here's another thought: consider using a flash, with a flash extender, for at least fill flash. That will let you use a slower lens and lower ISO. A cheap, lightweight option is the Rogue Safari:
https://www.pentaxforums.com/forums/22-pentax-camera-field-accessories/256288...-extender.html I'm using mine with the 55-300 and have been getting good results up to about 10-12m. The main catch is that your shutter speed is limited to 1/180th second, which is OK if the subject is stationary but not so good if it is moving. The only way around that would be to use an external flash with HSS and a flash extender (Bettter Beamer or similar).
---------- Post added 04-24-16 at 08:50 AM ----------
Originally posted by chibae My primary photographic focus is livestock portraits. Mostly horses but I have also done cows, swine, etc. For this I use a K5 with a Tamron 70-200 f2.8 lens.
A 300mm prime would be great for this too. If you bite the bullet and get the F/FA*300 f4.5 you would have one of the best lenses Pentax ever made. Sharp, minimal CA, light enough to use handheld, full-frame capable, and without the reliabilty concerns of the SDM motor in the DA*300. And wonderful whenever you point at a bird instead (with or without TC).
BTW, I hope you'll share some of your farm animal photos in this thread:
https://www.pentaxforums.com/forums/26-mini-challenges-games-photo-stories/29...m-animals.html