ISOs (incentive stock options) can be closed out in a cashless transaction. Say the first round vests, 25,000 shares. The stock is worth $7 but your option is to buy at $5 as you say. The broker executes and sells, you get $50,000, with no up front money. Edit based on comment below - you know they vest over 4 years, but how long before they expire? It stands to reason the longer you are able to hold them, the better a chance the company succeeds, and the price rises.
The first google hit forarticle Understanding employer-granted stock options (PDF) offers a nice document showingdiscussion of different scenarios supporting my answer.