Hire a real engineer like me to create the Gerber files and a Bill of Material/Parts List.
Send that to a turnkey manufacturing house, they buy all the material, install the parts & solder, put in ESD bags if that's part of your instructions, and return to you for testing.
With 5,000 you can send the .hex file and fuse byte info also and they buy programmed parts to put on the boards.
Or, you buy the parts & material, drop ship to an assembly house, they assemble & return to you. You have the parts house program the parts (ex. Digikey will do programming). They return to you for test.
Or, you buy the parts & material, send to an assembly house, they assemble & return to you. You program & test.
Place like cbas-usa.com in CA will do #2 & 3. I have used them successfully for #3, 50-lot has been my largest order.
Larger companies will do #1 as well.
All starts with designing the PCB from your schematics. With 5,000, I'd seriously consider a small batch, 5 or so, to start to check out & run for a few days. Option #3.
Then when you have all your design files finalized, can get quotes for #1. Make them responsible for procuring all material & dealing with suppliers.
Might consider an automated test box as well so you can quickly check each one out, depending on how complex it is.