Why won't the GUI close? Its keeps counting.

It's because you're using a for loop but not including this bit into the loop:

frame:TweenPosition(UDim2.new(-1,0,0,0),"In","Quart")

Since that part isn't in the loop, the script won't read it.

Edit: Though you don't need the for loop, I believe. so the new piece of code would be this:

local frame = script.Parent
local text = script.Parent:WaitForChild("TextLabel")


    text.Text = "Loading Story Mode (1%)"
    wait(1)
    text.Text = "Loading Story Mode (5%)"
    wait(1) 
    text.Text = "Loading Story Mode (15%)"
    wait(1)
    text.Text = "Loading Story Mode (20%)"
    wait(1)
    text.Text = "Loading Story Mode (25%)"
    wait(1)
    text.Text = "Loading Story Mode (30%)"
    wait(1)
    text.Text = "Loading Story Mode (35%)"
    wait(1)
    text.Text = "Loading Story Mode (40%)"
    wait(1)
    text.Text = "Loading Story Mode (45%)"
    wait(1)
    text.Text = "Loading Story Mode (50%)"
    wait(1)
    text.Text = "Loading Story Mode (55%)"
    wait(1)
    text.Text = "Loading Story Mode (60%)"
    wait(1)
    text.Text = "Loading Story Mode (65%)"
    wait(1)
    text.Text = "Loading Story Mode (70%)"
    wait(1)
    text.Text = "Loading Story Mode (75%)"
    wait(1)
    text.Text = "Loading Story Mode (80%)"
    wait(1)
    text.Text = "Loading Story Mode (85%)"
    wait(1)
    text.Text = "Loading Story Mode (90%)"
    wait(1)
    text.Text = "Loading Story Mode (95%)"
    wait(1)
    text.Text = "Loading Story Mode (99%)"
    wait(1)
    text.Text = "Loading Story Mode (100%)"
    wait(2)
    frame:TweenPosition(UDim2.new(-1,0,0,0),"In","Quart")
    wait(1)

Hope this helps.

You are not using the for loop correctly. What your code will do is load from 1% to 100% 5 times. If you want it to increase by 5% every second, you need to use the for loop differently. Here's an example:

local amtLoaded = 0

for i = 1, 5 do
    amtLoaded = amtLoaded + 5
    text.Text = "Loading Story Mode (" ..amtLoaded.. "%)"
    wait(1)
end

The for loop repeats whatever is inside of it the specified number of times. So in the sample above, it will add 5 to the variable amtLoaded each iteration and then change the text to the current percentage.