How do I make this water script slowly kill you?

You need to add a debounce if you want the part to damage the player every 1 second.

local Disabled = false --debounce

function onTouched(part)
    if not Disabled then -- If it's not disabled then
        Disabled = true -- disable :connect

        local h = part.Parent:findFirstChild("Humanoid") 

        if h~=nil then 
            h.Health = h.Health -5
        end

        wait(1)

        Disabled = false -- enable :connect
    end
end 

script.Parent.Touched:connect(onTouched)

There is actually a function for this!!

THIS WILL ONLY WORK IF YOU ARE USING TERRAIN WATER.

Here's basic code:

-- Put this in startercharacterscripts under starterplayer.

while wait(1) do -- Run every second.
    if script.Parent.Humanoid:GetState() == Enum.HumanoidStateType.Swimming then -- Check if they are in terrain water.
        script.Parent.Humanoid:TakeDamage(1) -- Take damage.
    end
end

That will only work if you are using terrain water as you say you are using water.