Congrats! 

But from the look of their rates for flight training alone, you will need a whole lot more than $5K. 

And if you want to fly professionally, I'd advise against "putting all your eggs in one basket", if the aviation degree program is what you're thinking of.

although they like to see applicants with college degrees,the kind of degree you get is fairly irrelevant to airlines. "Bachelor's in Pilot Stuff" doesn't count for much in that world, any more than having your first 100 hours logged in a new Cessna with a university logo on the tail and fancy new avionics, or an old one with peeling paint, a chronic oil leak, and 30-year-old radios. They also don't care if your instructors wore uniforms or dirty t-shirts. 

They mostly want to see that you are smart and dedicated enough to finish something like a 2 or 4-year degree (and maintained a healthy GPA), and have the minimum hours. Then, maybe, they might see about turning you into the kind of pilot they like to use. 

For you, the degree should provide you with a "fall-back" option. Even if you land an airline job, your continued employment is not assured and you will not make much money.
Imagine paying off loans for medical school while working as a burger-flipper... that's about what a new airline pilot has to deal with. And it's not getting any better. You gotta just love flying like a junkie loves heroin, or it is not worth it.

That's assuming you get hired, either as a pilot or some other aviation-related job... it might never happen. Without some other skills or degree, however, you'll face the same scenario (huge debt and lousy pay), but you won't even be flying. 

If I were younger and thinking about flying for an airline, I'd do my primary training as cheaply as possible, while earning a 2-year degree at a community college in something completely unrelated to aviation. I'd get my commercial before even my IR, so I could build hours flying banners or whatever while actually getting paid for it.

That would leave me a little money left over, so I could actually have beans with my rice for the next 10 years until I get a left seat and a little bump up in pay. Then I could maybe have a hamburger once a week.

But I'm not trying to discourage you, and you don't have to listen to me... ask some airline pilots.

Personally, I would probably set my sights a little lower than that as well, with minimal hours with a CPL, and a multi-IFR, you'll be lucky to find such jobs. Best bets are to become an Instructor, or to work for small bush flying operations. Also, I suggest looking into subsidized flight programs. They exist here in Canada, so they probably exist through-out the US as well. For instance, at my college, all I pay for is tuition, a normal college tuition, usually just under two grand, a semester. And that's on top of living expenses, but everything flying wise is paid for by the government (and no it's not military and I have no obligations to the military). The only flying things I had to pay for were my headset, various maps and stuff, and I have to pay for flight tests and ratings, and medicals... so... that's really not a whole lot in comparison to starting flight training with nothing, and finishing with a Multi-IFR. In any case, you should check into subsidized flight programs. They probably exist.