For that shot, I think your best bet is to film when the shadows are not encroaching on the tee and fairway like that. There is no amount of post-processing that can make that look good; camera sensors simply can't properly expose both those shadows and highlights.
PS Can you tell me what course this is? I have an abiding interest in golf course architecture.
Thats a good question.
Without getting way too technical, your camera, video or still, will attempt to calculate the F Stop (how much light) and the Exposure (how long do we illuminate the sensor) (or film).
You image is a toughy. Color film has a very narrow range of exposure. B/W, can become very wide. Digital sensors are another animal. Some narrow. Others really wide. By creating 5-7 images of a scene with various exposures and then grabbing shadow detail from one and highlight detail from another, a digital image can look really great.
Unfortunately, you are probably using Auto and creating a JPG as a result.
Kodak discovered the average 'scene' reflects 18% of the sunlight. In Auto Mode, your camera does the same. Usually losing detail in shadows and also the highlights.
A JPG produces a smaller image than the camera sensor can produce. It does this by taking surrounding pixel values and averaging several into a single pixel.
A RAW Image is a 1:1 ratio of pixel count on the sensor to the File produced. Your program takes that data and produces a JPG or TIF or whatever, you have a great deal of latitude to 'stretch' or 'collapse' the exposure given.
So, what to do?
An easy solution is to leave it in Auto and live with it. Another, use Manual exposure and set the ASA Speed, F Stop and Exposure yourself. Favoring shadow or highlights. RAW gives you the data and you can produce one image for the shadows, another for highlights etc. Then blend them together. In photoshop etc. But that means a great deal of Post Processing time on a computer to make that happen.
When I was shooting film with an X3 (which has inherently less dynamic range than the X5), I wrestled with the same conundrum. My choices were clear. Either blow out the sky or crush the shadows. N.M. has a gorgeous sky, so I didn't want some editor cursing at me for blowing it out. So I asked an experienced DP veteran how I should deal with that conundrum. His exact words; "F*** the sky."
It's way easier to replace the sky in post than it is to fix crushed blacks. So my trick was to tilt down and aim the camera at the subject matter sans sky, adjust the EV using the histogram, and then frame the shot the way the DP wanted it. He understood my choices were to either ignore the blown out sky completely or adjust exposure (stop down) *slightly*. I never received any grief for blowing out a sky. Conversely, I received a LOT of grief for crushing the blacks. It's all about compromise. Use common sense favoring your subject matter.
UPDATE: Your syntax "when shooting" doesn't specify video or stills. I always assume video, as stills are so easy to expose with RAW or HDR (bracketing) or a combination of the two that I just assume nobody would ask such a silly question. So my answer stands because I assume you're talking about shooting video.
UPDATE 2: I'll second what Niki says. Always shoot in Log, which would be D-log on the Inspire 1. I forgot to mention that.
For shooting video use d-log color profile (flat color) then in post by using davinci, aeffects, or premiere apply d-log to Rec709 conversion LUT but before that use your own adjustment curve or shadows/highlights adjustment while looking trough the applied LUT. At the end you may use slight denoiser to get rid of the noise in the shadowy areas.
For photo use RAW DNG and adjust shadows and highlights in post processing app like lightroom or photoshop.