Yeah definitely more than a Medium.
I am 5"8 and 60Kg, I ride a Large Giant Glory and it fits me perfectly so I think that the Large would fit you best.
Age is also a factor when choosing your frame. I'm 15 so it's better to get larger frame because of growth spirts etc. The last thing you want is to get a brand spanking new bike and have it be too small and a few months time.
I would say a Large would be a better fit (at least with a Giant) but look at the brand's website, all bike manufacturers have sizing charts so check them out because all manufacturers have different sizings.
Good luck with you bike.
Cheers Kyle.