Roma,
I see no reason that you shouldn't be able to put together a decent little
system for $5000. The EV powered speakers are excellent and aren't that expensive. I have several EV ELX112 powered speakers. Most of mine were bought brand new for under $400. There are sellers on the web that have great prices on EV gear. I use them over the EV ELX118p subs.
I know several sound providers that use the Behringer X32
mixer. For myself, doing theatrical work, I prefer to have all my
channel faders available at the same time. In my 20 years of experience, I've discovered that there are situations when I don't have time to
switch banks in order to access
channel faders during a show. Sometimes there are actors coming and going in rapid succession. I went with an Allen & Heath Qu32 (excellent
digital mixer, btw!). The A&H Qu16 can be found for under $1800 and might be a great fit for you.
I normally provide a full
system, as most gyms/auditoriums/schools don't have a great PA
system. I do have some clients that have a professionally spec-ed and installed
system and in those cases, I'll generally tie into their
house system. Works great for me. Just be sure to have any cables/adapters that you might need to connect into the
house system.
Best of luck!
Joel
Glaser Audio Productions