I havn't done much video shooting myself - and I don't know what video control's the K-5 has, but I'll try and give a few pointers.
Firstly, do some research and planning. Take a look at some gym video's online that match the style your going for and note down what you like about them/try and determine how they were shot. Try story boarding your shoot or at least note down how you think the final cut should be, maybe even include some timings. E.g. Opening shot -> wide shot outside of gym -> cut to close up of logo -> establishing shot of inside -> bla bla bla bla. This'll give you an idea of what shots you need to get, and it'll be a good reference point for when you're editing - you don't want end up with loads of random footage and then try to edit it blindly into some mish-mosh video.
Take long wide shots to use as masters and then shorter close-up clips to cut away to. Try to refrain from hand held shots unless they're close ups/faster cut aways, especially if you don't have a hand-held rig of some sort. Lock-down the focus on your wider shots and use a tripod for them - you can do some slow panning etc for a bit of movement. Don't try to force excitement into a shot by moving the camera around fast, as it can look amateurish and you'll probably get some bad rolling-shutter effects - instead use fast and short cuts, along with an energetic soundtrack, if you're going for "fast action". It'll will look cleaner and more professional than fast camera movement. E.g. short, static cuts of different parts of a moving exercise bike (gears, pedals, display) will look far better than one looooong shot of you moving around a bike.
If you're doing an interview with somone, it's probably best to use a tripod and have them sit/stand on the left/right 3rd of the frame with either a plain background behind them, or knock the background out of focus with a wide aperture. Again, maybe use this as a master shot - keep the dialogue running while you cut-away to some action shots -> then back to the master -> cut away, repeat. Also, when you're asking questions/they're talking, remember they'll probably be looking at you, so make sure you're standing by the camera or wherever you want them to be looking.
Know who your video is for - if it's a modern gym for younger people you'll have more skope to use interesting angles/experimentation/effects etc. if it's a more conservative place you'll want to refrain from pushing the boundries and just go for more of a conservative style. Talk it over with whoever it is you're making the video for and then gauge how far you can push it.
In terms of technical details, you'll want to to flatten out the in-camera settings as much as possible and then add any contrast/colour adjustments back-in during post. Try to get an even exposure across all of your shots, and refrain from using auto-white balance, set it to whatever wb looks best for the location your in and leave it there until you change location/the lighting changes. You won't have much leniency with jpg compressed video footage in terms of colour and exposure, so if you underexpose, don't expect to be able to pull it back without noise/issues when trying to match the rest of your footage, similarly if you mess up white balance for a shot, you might have trouble correcting it later. Don't go too high with your shutter speed or it'll look like a home-video, remember you're not trying to get pin-sharp frames like photography, you want to keep the motion present - try to keep it at 1/50 or so, and keep you're video frame rate the same for all of your footage. For everything else, just follow the rules you'd use for photography and you'll be fine - rule of thirds, depth of field to draw the viewers eye to your subject, lighting, and so on.
A tip for smooth panning on a tripod. Use an elastic band.
Put the band on the tripod panning handle (if it has one), or the camera lens, and smoothly drag it across trying to keep the speed steady as you move. Also for focusing, you can wrap a band around the focus ring on your lens, and mark down focus points in it with a pen - this can make focusing a lot more precise. For example, say you have a static shot of treadmill display, and you want to start out of focus, and then pull it into focus - firstly focus on the display (this'll be the end of the shot) and mark it on the band, then turn it out of focus for your starting position - press record, move the focus ring to your little pen mark, and boom, focus will be spot on.
Time-lapses can also be a great way to spice up footage.
There's endless amount of things you can think about, but hope that helps a bit as an overview. Any questions give me a shout, hope I've made sense with all that.
WoJ