First of all, the $5000 in government fees are:
$550 for check-ride (FAA examiner, not related to flight school). There are 7 check -rides for PPL, CPL, IR, MEI, CFI, CFII, MEI
$100 for each of the FAA theoretical exams (also, 7)
$130 for each of the TSA requests (there are 4: PPL, IR, CPL and CFI)
$100 for SEVIS fee
$100 for FAA medical
$130 for USCIS visa fees.
Further about the visa:
you can absolutely apply for a visa on your own. Will it be accepted or rejected? Thats. up to the consulate. Aerocadet provides support paperwork to ensure that your visa is approved. You can roll the dice on your own, no problem. But why do this, if their services are FREE?!?!
Also, none is asking you to pay for flight training in advance. In fact, it's not permitted. Students are requested to pay in 4 stages: initial deposit, then around $15000 after arrival, then $1500 3 months later and so on. (By the way, I agree - don't pay for the flight training in advance)