For outdoor portraits on a D5200, the 50mm f/1.8G is generally the better choice. On Nikon DX it gives a field of view similar to about 75mm full-frame, which is a classic portrait range and usually more flattering than the 35mm’s roughly 52mm equivalent view.

If your goal is stronger subject isolation and more background blur, the 50mm will usually give more bokeh than the 35mm when framing portraits similarly. It also fits the common recommendation that portrait focal lengths start around a 70mm equivalent and up.

About sharpness: an FX lens on a DX body can sometimes look very good because the camera uses the center of the image circle, but that does not automatically mean it will be “extra sharp.” Lens design matters more than the FX/DX label.

A practical check is to look at portraits you’ve already taken with your kit zoom and note which focal lengths you naturally use most. If they tend to be above about 40mm on the lens, that points toward the 50mm prime.

So if your main purpose is outdoor portrait photography, the 50mm f/1.8G is the safer pick.