How can I let the script know when the player has held down a key for a certain amount of time?

You can combine checking for key down and key up with an update loop that keeps track of the time the key has been held to do what you need. Something like this:

local UIS = game:GetService("UserInputService")
local RunService = game:GetService("RunService")

local RunningSound = 'rbxassetid://4518544160'
local WalkingSound = 'rbxassetid://156659098'
local running = script.Parent.HumanoidRootPart:WaitForChild("Running")

running.SoundId = WalkingSound
running.Pitch = 1.5

-- Variables used to detect key being held down
local isShiftDown = false
local keyDownTime = 0
local triggerTime = 5 -- Seconds that shift needs to be held

RunService.Heartbeat:Connect(function(step)
	-- While shift is held, increment keyDownTime and check if we exceed triggerTime
	if isShiftDown then
		keyDownTime = keyDownTime + step
		if keyDownTime >= triggerTime then
			-- Shift has been held for >= triggerTime. Change sound id
			running.SoundId = RunningSound
			
			-- Reset isShiftDown so that the code here doesn't keep firing while shift is held
			isShiftDown = false
		end
	end
end)

UIS.InputBegan:Connect(function(input, gameProcessed)
	if input.KeyCode == Enum.KeyCode.LeftShift or input.KeyCode == Enum.KeyCode.RightShift then
		-- Shift is held
		isShiftDown = true
	end
end)

UIS.InputEnded:Connect(function(input, gameProcessed)
	if input.KeyCode == Enum.KeyCode.LeftShift or input.KeyCode == Enum.KeyCode.RightShift then
		-- Shift is released
		isShiftDown = false
		keyDownTime = 0
	end
end)