"how do we know where on the fretboard the specific key is on. For example, if the key is in C how do I know the root note could be 3rd fret fifth string and not 5th fret 3rd string?"

Whilst everything Schlegal said is correct (of course)

a simple answer is:
The "and not" part is erroneous assumption on your part.
Key doesn't change depending on how low or high the particular C is.
(so it doesn't matter at all which C you choose)
(beyond your own aesthetic preference)

They 're both Cs.
(it's just that one is C3 and the other is C4)

The choice of what C you choose is the same thing as deciding if you want to sing high like John Mayer; or lower like Muddy Waters or whatever.

My advice:
Don't concern your self with trying to understand this at this point.
Just absorb music theory lessons about scales and song keys and eventually it'll make more sense to you.
(Trust the process: absorb... apply... understand)