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Score of 710 looks good.
Income of $18,000 a year could be a challenge but never say impossible.
Get that CC utilzation way down, your scores should go up. Many would say 1 card reporting between 1 and 9% utilization.
The $5,000 down payment is 20 - 25%, good.
For example Hyundai has a first time buyer program. A few qualifications they list: (see bottom of post for more info)
At least $1000 down, check.
Minimum 6 months on job?
No previous secured loan (like an auto loan), check.
Up to 72 months, check.
Looks like payment can be 15% of gross (before taxes) income. $1500 X 0.15 = $225 payment.
Example: Your car $20,000 + dealer fee $299 (varies greatly) + Tax (this based on 8.5% sales tax) $1,700 = $21,999
$21,999 (total price) - $ 5,000 (down payment = $16,999 (amount to be financed)
$16,999 financed for 72 months at 0% interest (not likely) = $236.10 a month.
$16,999 financed for 72 months at 5% interest = $273.77 a month.
$16,999 financed for 72 months at 10% interest = $314.92 a month.
Don't forget about insurance, and at your age will be high. And please don't let it be a Mustang or you might really be looking at a huge insurance bill.
My car buying advice for you:
Do not go into the dealer unprepared. There are plenty of resources on the internet. Read, read, read and ask questions. Google 'car sales training videos' and watch some of them. Knowing the techniques that will be used to 'sell' you can help prevent over-paying.
Do not let the dealer run your credit as you are shopping. Some dealers will 'shotgun' your application (could get 5-10 inquiries as they shop for a loan).
Look for a less expensive car. If you find one for $17,000 (the price you negotiate) You could be paying $203.87 for 72 months (5% interest & $5,000 down).
Find an experienced car buyer to take with you (Dad, uncle, someone who understands the process).
Many here would say find a car for $5,000 and never have a payment ( I can't disagree). If you go this route pretend you have a payment and put that payment in a savings account each month. In a few years you will have a nice balance in your account.
Sorry for such a long post, I am just hoping that you can learn from the mistakes that many of us have made when buying cars.
If you have questions, ask away. Let us know how the process is going.

And I do not work for Hyundai, just wanted to provide an example. What car are you looking at by the way?
If you can get an auto loan from DCU, good on you. They have some of the best rates I have seen.
Kuma,
On the Equifax FICO 5 for DCU is that Auto or Bankcard? At least I believe there is an Auto5 and Bankcard5 for Equfax.
Thanks