The answer to this is totally different depending on your pace and personal fitness level.

Most people who'd call themselves a long distance runner can run at least a 5k at a moderate pace without breathing hard. However, if you run a 5k at sub-5 minute mile pace, you're going to be very tired unless you're a very good runner. It all depends on how hard you push yourself and how fit you are to begin with.

If you're exhausted by running a short distance like 1km, you probably just need to work on building up your aerobic fitness. Try running until you're slightly out of breath/tired, then walk a little, then start up and run 1km again. Do this for a while, slowly lengthening the interval you run.

It's also important to not try and go too fast right away. For example, running 1km in five minutes is a fairly fast pace for a total beginner. You might try running up to one minute slower and try to go longer, in order to build up endurance.