Based on the pictures and your description I think your mineral is beryl.
- The colour. Usually colour is not diagnostic of the a mineral type, but when beryls are green - they look precisely like this.
- Hardness. You say it's 7.5 so by that I understand that you mean it's harder than quartz (softer than topaz). There aren't many mineral harder than quartz than quartz that look like this. Beryl is one of the more common.
- The crystal shape. Beryl is commonly elongated just like yours, and it's hexagonal. The last picture clearly shows that it is hexagonal.
- It just looks like beryl. Sorry for being non-scientific about it, but with some experience you learn how some minerals look like. And this one looks like beryl.
Other things it can be but I don't think so:
- Apatite. Hexagonal, green, but softer than quartz. Usually more smooth, or if not, is not translucent.
- Tourmaline. Extremely rare to find non-black tourmaline. Doesn't have the characteristic striations.
- Spodumene. Should be octagonal, not hexagonal. Looks a lot like this one though.
I would add that this could also be plenty of other more exotic things I haven't thought about. May be beneficial to take it to a local mineral club, geologist, geological university department and ask them. They might be familiar with the local geology and give you a positive identification.
It's also a nice specimen of beryl (if it is indeed beryl). Not museum quality, but quite a rare find. Enjoy it!