I'm super glad that you're not worried about your weight under normal circumstances! 
However, losing 5kg in a month is very unlikely, I doubt there is any safe way to accomplish this. I'm sorry that's probably not the answer you want to hear, but I do know personally how difficult it is to lose weight as I'm on a bit of a journey myself! And I can tell you--even just hitting 1kg a week consistently is hard work and I am much heavier than you are (meaning I lose weight easier). To sort of give you an idea of the biology behind it, although metabolism is pretty complicated it's generally accepted that you need to be in deficit 37,000kj (8800 calories). So it's a huge undertaking to lose 1kg a week (and you're aiming a bit higher than that!), and the smaller you are the more difficult it is.
It's probably best to explore other options--can this dress be returned for any credit? Can it be tailored to fit you? Are you able to buy another dress if you can't wear this one (are there any time or money constraints)?
Hopefully other forum goers can help out!