How to temporarily scale a Wordpress site?

Hi there,
I'm trying to address a concern of my customer running the website mentioned above. They will be on a TV show and expect a sudden, temporary load increase during the show and a few days following.

I'm still trying to quantify that "load increase", but maybe you could help me identify an appropriate option to prepare the infrastructure.
Right now the site is hosted on a VPS together with 20 other sites, none of them creating a traffic that would be worth mentioning.
As the load increase will last for a week at maximum, I don't want to throw hardware at it. Using AWS and a load balancer seems to be the better option.
The users may fill in some contact forms or sign up for newsletters, but there won't be huge down- or uploads and the website itself will not change during the time.
Do you have any idea what the most effective approach might be? And where to find corresponding tutorials?
Would it be ok to have multiple instances that all have their own mysql instance?
Or do I need to run a shared MySQL instance that is used by all webserver instances?
If we are looking at e.g. 5000 concurrent users, does load balancing make sense at all or would a large, powerfull EC2 instance be sufficienct?
Maybe together with a CDN?

As you can see, I'm at a loss right now where to start and in which approach I should invest time to investigate and test a setup.
Especially as I didn't have to deal with any high-load sites so far.
Maybe you guys with all your experience could point me to the right direction :slight_smile: