I don't know the specifics of these led's but when I connect them to 5V they don't burn out (though they get very hot) but when I connect them to Digital 5 instead of shining with full power they are barely glowing
A current limiting resistor is absolutely required with LEDs. 150 Ohms minimum for a red LED.
You can burn out the Arduino as well as the LED, if you leave it out.
Maybe you shouldn't use them. 
Maybe they are infrared or ultraviolet? (With a little light in the visible spectrum.)
A "high power" LED is sometimes multiple LEDs in series so they require more voltage but I wouldn't expect them to get hot and also be dim at the same time.
High power LEDs normally need a heatsink.
In general, LEDs are "current operated". Feed them the correct current and the voltage "falls into place". With "regular little" LEDs we can use a resistor to control-limit the current but high power LEDs normally use a special constant-current source.
Wire LEDs as D1 or D2.
In the Arduino IDE, use Ctrl T or CMD T to format your code then copy the complete sketch.
Use the < CODE / > icon from the ‘posting menu’ to attach the copied sketch.
Did you set the pin to OUTPUT with pinMode().
Leo..
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