is it possible to get $5k line of credit with $10k annual income and 700 score?

Nope, you'd probably get in the range of $300 to $3000, depending on what credit card you applied. If you're in the range of 18 to 20, you must provide proof of steady employment and/or co-sign with an adult 21 years or older with good credit and a steady job.

The first time I applied for a credit card many years ago (I made a little more than you working PT), and the limit was $2000.

No. You have to have an income of at least $35,000/$40,000 and be employed 12/18 .