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Yes, you can get a credit card with a limit of $5,000 to $10,000, as long as you meet a few requirements.
First of all, you should have a pretty high credit score to get a limit above 5K - if you have an excellent score, your chances of getting a high credit limit are better. A score in the very high 700s† or the 800s† is ideal.
Secondly, your income should be high enough to show that you'll be able to pay off a higher balance, or at least make minimum payments on a high credit card balance. Of course, it's best to pay off your balance in full each month if possible, but if you're carrying a balance then you should keep in mind that minimum payments are usually between two and five percent of the total balance. That means if you run up a balance of $10,000, your minimum payment will be between $200 and $500 each month. A credit card issuer will want to know that you can afford to make that payment comfortably.
If you don't have a stable income or credit score high enough to get a credit card with a limit in the range you want, don't despair. There are lots of good credit cards with lower limits, and if your income or credit score get a boost, you can always call your card issuer and request an increase in your line of credit. If you've shown that you can handle credit responsibly and your income is enough to pay off your debts, your limit could be lifted.