Yes, it's true. For any number larger than 5 (call it 'x'), you can always find a value of n such that x is not in the interval [1,5+1/n). Therefore, it becomes a closed interval [1,5].
Another way to say this is:
Suppose that I have an half open interval, .
Is it correct to say that the half open interval will become a close interval, as n approaches ?
My thinking is that to the right of the number 5 changes, but it could never affect the number 5. In essence, at the end the interval will be . If I drop the , I will still get [0,5].
I am not too sure. I need help.