The 750K5 powers the headlight thru the START switch on the right handlebar, when the START button is NOT pressed. It thus turns the headlight OFF when the START button is pressed, to make more battery power available to the starter.
If the headlight was converted (in the past) to a high-power halogen bulb (80 watts or more), this melts the START switch (warps it) so it will not power the headlight anymore when it is not pressed. This is very common in the K4-and-later 750 (and 550, too).
Look at your fuseholder and note the 2 wires coming from the middle fuse: these will also be the 2 wires in the middle of the plug from the fuseblock. They will be (usually) Brn/Red on both sides or Blk/Red on one side and Brn/Red the other, depending on when your 750 was built (i.e., before or after about 3/75). With a voltmeter, test the middle fuse for power: if it does not get power when the key is turned ON, then the START switch is likely melted and warped.
If so, you can bypass the START switch by connecting the wire that is connected to the LEFT side of the middle fuse directly to the Brn/Red (or Blk/Red) wire in the headlight, and connect the wire from the other (left) side of that fuse to a BLK wire in the headlight (there should be a spare socket or two in there, or you can use one of the 2 that go to the Start switch - you'll know if you picked the wrong one because the START button won't work: swap them then. This will power the Lo/Hi switch on the left handlebar, but will leave the headlight on during START, making the battery's job a little harder.
If the headlight bulb is more than 55/60 watts, get a headlight that is within that power, or less, to prevent it from damaging other wiring in the future. Even the 55/60w type will slowly [re]melt a new START switch, even if it is replaced. I offer a special START SAVER RELAY kit to prevent this from happening with hi-power headlights, and it can be used in situations like yours if the START switch has melted and you don't want to change the switch.