I wanna go backpacking across Europe!?

you must add Prague, Venice, Monaco, Vienna, and much much more! keep researching you've still got 3 or 4 years and there are just TONS of places you should visit when you go to Europe. If you're staying for 5 months and in a hotel, that will reallly cost A LOT of money. Seriously, I'm not sure exactly how much it would cost, you'd have to research everything like hotel fees, train fees, food fee, etc and calculate it but it will surely cost much more than $10,000 soo..if ur rich that's fine but if not, you better start saving up money! If I were you, i think it would be enough to just stay in for like...2-3 months.