Spence,
Your example (5 and 10 limit) is for the $10 betting round, so the option you listed is for a RAISE to $18, not a bet because the next player can just call the $8 all-in. I will go back to the original limit game (2 and 4). On the $2 betting rounds (pre-flop and after the flop) players must bet $2 and can only raise in incriments of $2....so with a three raise limit the cap on a $2 betting round is $8, the initial bet ($2) and three raises. A better example to help you understand the raise rules for limit games is on the $4 betting rounds. Lets say that Player A initiates the $4 bet on the turn and the next player goes all in for a total of $5. The option to the next player is to call the $5 or complete the raise to a total of $10 (because the $1 raise from the all-in was less than 50% of the required amount). Same situation; Player A bets $4 and the next player goes all-in for a total of $6 or $7 (both are 50% or more of the required raise amount), the options to the next player are to call the $6 or $7 all-in, or make a full $4 raise above the all-in amount. They can not complete the bet to $8 because the increase from the all-in player is recognized as a full raise. Limit games usually have a 3 or 4 raise limit, so the all-in player can affect the "cap" for a betting round.
I would like to see this raise rule applied for no-limit, IMO, it is much easier to understand. Spence is correct when he says "It's a good idea to familiarize yourself with the house's no-limit raising rule before your get involved in a big pot."