If it takes you that many engineers you are either using the wrong software or using it incorrectly.
Adding to other large company problems, these people will need management layers, the team will need a charter for growth. Who wants to be the maintainer of the Mattermost servers in a large company? Add all of this up and then the slack deal starts to look reasonable.
Edit: Just to add some real numbers, slack costs $12.50 per user per month [1] - that is ~$750k per year for 5000 users = 5 engineers. (More like 3 really in the Bay area)
There's no way it suddenly needs a new team of dedicated full time resources.
There's no way a company with 5000 Slack users is paying the sticker price per head - they'll call Slack's enterprise sales team and negotiate some volume discount with whatever shiny enterprise-grade features, SLAs, support guarantees, etc. they need.
Moreover, email is hard and does require a dedicated team, but the order of magnitude is wrong here. 5 people is plenty.
These Bay Area tech people must be either incredibly inefficient (especially when comparing to what they get paid), or your estimate must be waaaaay off.