Fuji S5200/5600 -
Actual focal length, 6.3mm - 63mm
35mm equivalent, 38mm - 380mm
A 35mm lens of 6.3mm with an f3.2 aperture would hardly even need a focus ring, it's depth of field would be enormous - that still applies if you mount the lens on a camera with a tiny sensor. It gives you the field of view of a 38mm because the sensor is smaller, but it still has the optical characteristics of a 6.3mm lens. As JimC so clearly states, the 380mm (63mm) end gives you much less depth of field but remember, optically it has the DOF characteristics of a 63mm lens but due to the small sensor it has the field of view of a 380mm lens, it therefore must be used at greater distances and thus looses the DOF advantage.
On the plus side, you can use software to blur backgrounds but you cannot make an out of focus shot sharp. The greater DOF of these cameras will mean a much higher percentage of sharp pictures.
Let me add one illustration, we have your camera, an APS-C sized sensor DSLR (typical) and a 35mm camera. We want to cover the exact same field of view from the exact same distance (in other words all three picture will show the same subject from the same perspective). You set your camera at its widest focal length, 6.3mm, the DSLR is set at 25mm and the 35mm is set at 38mm, all pictures are shot at f4. The framing and perspective are now exactly the samebut theresulting pictures will be very different, yours will be sharp front to back (unless we were very close), the DSLR will have much more limited DOF with a somewhat out of focus background and foreground, the 35mm will be noticeably more limited with the background now significantly out of focus.