Why doesn't this change the team or kill me?

Here, try this.

local sign = script.Parent
--You didn't need to connect to the new player, if you're using a click detector then the event will automatically get the player, just add plr in the parenthesis of onClick
local ding = false

function onClick(plr)
    ding = true
    local peopleonblue = 0
--As for the checking the number of people on the team you could do the following code;
    for _,v in pairs(game:service("Players"):children()) do --It says don't use children or service in new works but it still works the same way (I made a question about children and GetChildren, no one answered).
        if v.TeamColor == BrickColor.new("Really blue") then --If the teamcolor is really blue then...
            peopleonblue = peopleonblue + 1 --Then count him/her as being on blue team.
        end --End if statement.
    end --End the loop
    if peopleonblue <= 5 then --If there are less than 6 people on blue team, it will do what you want the script to do to them.
        --Do what you need
    end
    plr.TeamColor = BrickColor.new("Really blue")
    wait(3)
    plr.Humanoid.Health = 0
    ding = false
end

sign.ClickDetector.MouseClick:connect(onClick)