Spot light LED bulbs (MR16) flash once when turned on. If I put 1 normal halogen in then it solves the problem. Why?
This symptom is impossible without silicon electronics being involved in the delivery of power. Passive wires and windings are not capable of causing this.  Common problems are common, and my first take is usually correct - a series connected old-style smart device. 

But Carl Witthoft has an interesting theory: these are probably low voltage bulbs.  We know voltage is right because the LEDs do work properly when power is available.  That's not surprising, since many LED products use constant current power supplies in switch mode, which can easily accommodate a range of voltage.

Most low voltage power supplies are passive, or at least well behaved.  So I normally don't think about them.  It would certainly explain everything if you had one that was "too smart for its own good".  The five LEDs should draw power comparable to one halogen (at least on half the AC cycle... since the D stands for "diode"). So there's clearly something a little more sophisticated going on.  I could see some power supply designer thinking himself oh, so clever for adding a protective circuit that shuts the supply off if it doesn't detect any halogens.  To be fair, LED lighting is a very new concept. 

For reference, the usual cause - and my first guess - and the one to apply if this proves to be 120VAC circuit -- relates to dimmers, sensors and other smart devices designed to substitute for an old switch in a "switch loop", where there is no neutral.  These devices place themselves in series with the bulb, and power themselves by letting some current flow through the circuit when the light is "off".  This depends on particular characteristics of incandescent (and halogen) bulbs.  It often doesn't play well with fluorescents and LEDs.  This is why Code now requires neutral in switch loops - so a new generation of these devices can power themselves directly off hot and neutral.  For this, the answer can be to roll back to a plain switch - unless neutral happens to be in the box, in which case use a modern device.