In no particular order, except for No.1
1. My No. 1 bit of advice: Learn your camera and practice practice practice until you can operate it without thinking or looking at the controls. Practice in all possible shooting conditions (bright sunlight, shade, indoors, close-up, panning, changing focus) until it's absolutely second nature. Did I mention practice? And BTW, I'm assuming you already know the basics, such as the relationship between aperture, shutter, and ISO, how to determine depth of field, etc.
2. Keep it steady. I've spent at least as much money on stabilization as I have on my cameras.
3. Buy a variable neutral density filter or matte box with filter slot and assortment of ND filters. Control of exposure via filters is absolutely essential for outdoor shooting, not so much for indoors.
4. Focus is critical. Either set it deep or double/triple check your focus via high magnification, focus peaking, etc. Buy a loupe or an HDMI monitor with shade if you plan to do any outdoor shooting. I'm lousy at follow focus, so perhaps others can provide advice on that art.
5. I'm a real hack at audio, but it's obviously terribly important. Get a hot shoe mount mic at the very least, and turn off AGC if possible. Better yet, get the mic off camera and record into a proper external preamp and recorder. Do this even if you don't intend to use the audio from your shoot - you never know where your creative mind will take you once you start putting it all together in post.
6. Plan what you want to achieve before you begin - preferably long before. Develop a shot list, storyboard, or whatever scheme works for you to make sure you capture everything you need. There's nothing more annoying, if not terrifying, than realizing that you overlooked a critical shot and can't reshoot. And don't make the mistake of thinking that you don't need a shot list or that your shoot can't benefit from one. Even a vacation video can be planned (WA establishing shot of resort, close-up of birds on beach, sunset with silhouette of wifey, etc.)
7. Remember that you always have a higher opinion of your work than others do. Get over it, swallow your pride, and try to learn to critique your work with a dispassionate eye. You'll catch more glitches that way.
8. Know the limitations of the medium and work around them. For DSLR, it's crappy dynamic range, moire/alias, and rolling shutter (I'm not counting all-manual operation; in my opinion that's a benefit, not a limitation!). Avoid setups where these issues are problematic. Yes, it can be frustrating, but it can be done.
9. Get help. I primarily shoot solo, but the few times I've had assistance have been so much more enjoyable!
10. If you take advice No. 1, then Nos. 2 through 9 are unnecessary because you'll run into all the nasties on your own and work out your own solutions.
Sorry it's a few more than 5. And my list is really only for those just starting out; I'm definitely not qualified to advise on doing narrative filming with a full crew, talent, etc.