It should be taxed at your regular income tax rate - you received this in a sense as income so it will be at the higher tax rate (not capital gains) - which in your case would be your income tax rate. As this amount (combined with your annual salary) would not be any where near enough to boost you into a higher tax bracket.
That being said you may get more back than the actual tax rate depending on how many deductions you have.
To be safe (and then this would be a bonus after you complete your taxes) - put aside enough as if you were going to be taxed on your federal and state (local if you have any) tax rates.
The reason they tax at 25% for $5,000 and above is similar to any sort of bonuses paid out at the workplace. They assume your winnings (or bonuses) could boost you into the next tax bracket so you tend to taxed higher for these sorts of things. Although my bonuses are always taxed at 42% - I get a good part of it back though when I file my returns. So this could be they take out 25% for the state only and not take out for federal since it is a state lottery (state wants to make sure it gets its money).
It is confusing all the tax rules, but considering your annual income and you have some deductions, you will be more than safe by saving aside your normal federal and state taxes.