I would save a few more bucks. 5k can go quick easy. you have a security deposit, all your utilities, then your actual rent, not to mention gas and food, health insurance since you will be without it. You could all the sudden have car issues and need repairs. 5k just doesn't seem like enough.
Before I got my job, I worked a third shift position making $12/hr and I applied every night all night. I sent out about 100+ apps and traveled about 5,000 miles in about 3 months before I finally snagged a position. To get a decent job now days, it takes dedication and committment. Plus if you want a solid job, they look at past work history and if you take a leap of faith and can't get anything and working as a bar back doesn't really make your resume shine. I would try to shoot for something near the states around you. Then if all else fails, and you really can't find ****, save up about 10k and then shoot for the stars and head over to ca.