SurfaceGUI to convert one leaderstat into another?

Your error lies in the fact that you wrongly assume that the cool and stuff variable are references to the actual property of the IntValue. If the value of the IntValue changes, the variables you have defined won't update; only its Value property will change. In order to fix this, you can remove the cool and stuff variables and only make direct accesses to the Value property of the IntValue. You could also modify the variables to hold the IntValue itself.

player = game.Players.LocalPlayer
cool = player.leaderstats.CoolStuff
stuff = player.leaderstats.Stuff
buybutton = script.Parent

buybutton.MouseButton1Click:connect(function()
    if cool.Value >= 5 then
        cool.Value = cool.Value - 5
        stuff.Value = stuff.Value + 15
    end
end)

It is important to note the difference between a reference and a value. Think of a reference as holding an actual memory location while a value just holds some normal information (such as a number). For example in Lua, tables are passed by reference.

local tableOne = {foo = "String" , random = 8 , goo = false}
local tableTwo = {foo = "String" , random = 8 , goo = false}
local tableOneRef = tableOne
--tableOne and tableOneRef both represent the same table now
--tableTwo is a different table

tableOne.foo = "Hello Earth!"

print(tableOne.foo) --> "Hello Earth!"
print(tableOneRef.foo) --> "Hello Earth!"

print(tableTwo.foo) --> "String"

The tableOne and tableOneRef variables both hold the exact same table or memory location while the tableTwo variable is a different table even though it holds the same values.

On the other hand, datum such as integers and booleans are passed by value.

local num = 5
local numValue = num

num = 10

print(num) --> 10
print(numValue) --> 5

Even when numValue is set to num, both of these variables have different memory allocated and thus changing one value does not change the other.