How do fire off an animation after a certain amount of time?

This isn't a request site so you should have the code you're having trouble with. Please keep this in mind in the future. Nonetheless, I'll attempt to answer your question. You haven't provided much in terms of framework for your animation, so I'll provide basic framework. As for the wait, just simply use wait().

local animation = Instance.new("Animation")
animation.AnimationId = "http://www.roblox.com/Asset?ID=144884906" -- replace the link with the link to your animation.

local animTrack = Humanoid:LoadAnimation(animation) -- humanoid needs to be a variable you create with the humanoid of whoever is being animated
wait(5) --time waited
animTrack:Play()

this just plays your animation. Doesn't specify conditions. Hope this helped.