This is probably a stupid question.
Let us say I were to prove something by induction. Is it true, that the basecase must be the lowest possible number? If I wanted to prove that the formula holds for 1, 2, 3, ... , 999 for example, the basecase cannot be 5 right? Logically, if it holds for 5, it does not necessarily hold for 4, 3, 2 and 1, correct?
On
With induction we usually prove something for all integers bigger than or equal to the base case value. If we show that a statement holds for $n=5$, and show that if it holds for $n$ then it holds for $n+1$, we have shown that the statement holds for all integers greater than or equal to $5$. However, nothing stops you from also using induction in the other direction: That is, also prove that if it holds for $n$ then it holds for $n-1$. Nów if we can show that the statement holds for an arbitrary base case, we have automatically proven it for any integer! (This form of induction isn't very common though).
The base case can be 5, as long as you prove the cases 1,2,3 and 4 in some other way.