Full service and $5k isn't easy, unless you are willing to really hunt deals. But it really needs to be based around what you are doing. Always building cages? you need a bender. Building one cage? - Buy a bender as part of the project and sell when done.
At a base I'd say:
Toolbox
Good set of sockets, wrenches, screwdrivers
Impact gun (I would get nicer than the base model home debt/blowes here - step up to the mid grade)
Good Vise (another place to spend a little, maybe used)
Drill Press
Good set of drill bits (super underrated)
Lighting, about 1.5x what you think you need
Welder - I like my AHP for the $$, can start as stick and add a tank later
Shop press (maybe save the brake for a project that needs it)
Battery Grinder(s)
Bench Grinder
Lots of hammers, including slide hammers
Pliers of all types
Multimeter
Funnels
compressor - don't need a big one unless you add a sandblast
Portaband
Workbenches
Probably forgetting a lot. But when I can spend $1k a year on consumables for shop work - abrasives, blades, bits $5k can get soaked up decently quickly. I'm a big fan of building tool purchases into project budgets