current versus voltage supply
You're right to be confused; 5V at 900mA is only 4.5W.

The specifications given are probably simply wrong. But it's hard to say for sure which parts of the specs are erroneous.

This is part of the reason why on EE.SE we like to say "No datasheet? No sale!"; With a proper datasheet, you have much more information at a higher reliability. Even if the datasheet is wrong (it happens), it's easier to speculate what the data should be, and it's easier to contact the manufacturer for clarification.

For example, it could be that 900mA @ 5V is the nominal rating, and 10W is a peak/pulse rating. Selectively quoted for marketing reasons. If this were so, it would be clear from a datasheet.

But honestly, these parts look like the usual cheap junk with unreliable specs you can find in droves in places like Ebay, DealExtreme, and AliExpress. There's no telling which of the specs actually make sense and which don't, and anyway the quality is a gamble. See also this answer.

You can buy that stuff and hope for the best, but you're pretty much on your own there.


  So, if I use a supply that is limited to 900ma, but says it is 6 to 10 volts, will that burn out the diode?


Well, assuming the 5V spec for the LED is correct, and so is the 6-10V compliance voltage of the current source, you'd be operating out of spec, and there's probably no guarantee what would happen. If there is something guaranteed, the datasheets will tell you.

But assuming correct specs, some possible outcomes:


The current source cannot go that low in voltage, and will shutdown (perhaps trying to restart periodically).
The current source cannot go that low in voltage, and will output 6-ish volts, resulting in a current that is too high, possibly damaging the supply or the LED.
The current source will go down to 5V, and everything works.
The current source will go down to 5V, but only just; any variation (in input voltage, LED temperature, etc...) will cause it to go out of spec and misbehave.
The current source will go down to 5V, but it doesn't like it and gets hotter than intended, maybe breaking eventually.


What to do instead?

The way I would go about this: buy something with datasheets from a reliable vendor, and design something that stays within the parameters outlined in both datasheets. That way you don't have to hope and pray.