Constant Current of an XL4016 Buck Power Module
I'll not comment on the specific device you mentioned for the reasons already clear on the comments.

Will my load receive 5A constantly or will the current limiting feature kick in once my load reaches 5A?

Ideally, a voltage controlled source with current limit would work like this:

If configured for 10V, limited to 5A, start from the blue dot, with no load connected. As the load is increased (you can imagine smaller resistors being connected) the current increases. When the current limit is reached, the voltage starts to drop if you keep increasing the load (reducing the value of the resistor).
Obviously, the lines will not be perfectly parallel to the axes on real devices and other limitations (like power, input voltage, minimum load etc) will be detailed on the datasheet.