what base number system is the hebrew language?

Actually, the values of the letters continue up to 90, then 100, 200, 300, and finally 400 for the tav (see the Wikipedia page on Gematria). (The values for the "terminal letters", like the nun-sofit, are, I believe, more "recent").

But this is not a base system, because the system is not positional, it is aggregate: the value of a latter/symbol does not depend on its position, the way it does in decimal, binary, etc., but only on the letter. So two words that are made up of exactly the same letters, though perhaps in different order, would correspond to the same value. This is not true of positional/base systems.

It's even worse than the Roman numerical system, because there are no positional rules here the way you have for Roman numerals.

The hebrew numerals don't have a base, because they're not a positional numeral system any more than Roman numerals are.

(There are some usages that reuse letters for values 1000 times as big. In that sense, it is base 1000, but that's stretching definitions a bit.)

Hebrew is an interesting number system that isn't in a base like ours is. Here is a link to wikipedia's article on the Hebrew numbers - the idea is that they just came up with new symbol for bigger numbers, like the Roman Numerals or Etruscan Numerals did.