For this call volume, you should really be looking at carrier class equipment rather than a bunch of FreePBX servers.
Your communications infrastructure will be the first limfac in your design. There are system out there that handle thousands of phones with hundreds of simultaneous calls. @arielgrin is right, though. Unless your devices are going to be using the same protocol as everything else the system will be connecting to, transcoding will eat your CPU performance alive.
Yes, you’re going to need a Class 5 switch and most likely a Class 4. However, maintaining 5,000 simultaneous calls would be that there are constantly around 700-900+ calls per second being made. This is breaking into the realm of carrier level services so not only would you need the switches, you need media servers, peering with Tier 1 carriers or being a Tier 1 or 2 level yourself, data center services and a high skill level team to deal with this. That’s just the broad strokes, more will be exposed as you start getting more granual with details.
This is going to be more than a few servers and some bandwidth. As Tony said, you’re going to need some serious investment not only in cash but time and resources.