Your D5000 has 3 auto focus modes - AF-S, AF-C, AF-A - PLUS 4 focus area modes - Single point, Dynamic area, Auto area, 3D-tracking. (pages 54-61 of the D5000 users manual).
The next consideration is depth-of-field (DoF) or how far from the camera the zone of acceptable sharp focus begins and ends.
How deep that zone of acceptable sharp focus (DoF) is is determined by several variable factors: the lens focal length, how far from the camera the point of focus (PoF) is, the lens aperture.
With a 35 mm prime lens the focal length stays constant and the PoF distance and the lens aperture become the main variable you can control.
So you want to take make a head shot type photo of one of your children
You pose the child so one eye is closer to the camera and you focus on that closer eye. You set the lens aperture to f/2.8.
Using an online DoF calculator, like
Online Depth of Field Calculator we plug in the pertinent numbers;
Nikon D5000
Focal length - 35 mm
Selected f-stop - f/2.8
Subject distance (actually PoF distance) - 4 feet
and the calculator tells us
Depth of field
Near limit - 3.79 ft from the camera's image sensor
Far limit - 4.23 ft from the camera's image sensor
Total DoF- 0.44 ft (5.28 inches)
In front of subject - 0.21 ft (2.52 inches) (47%)
Behind subject - 0.23 ft (2.76 inches) (53%)
If you don't pay close attention and lean just 2.75 inches closer and don't re-focus, that front eye will no longer be sharply focused.