It's not 5 billion per year when cap is reached, it's 5,256,000,000 after block 600,000. Right now block reward is anywhere from 0 to 1,000,000, when we reach block 100,000 it will halve and rewards for blocks will be 0 to 500,000.
The idea is that there can never be more than 100 billion dogecoin in circulation at any given time, but you want miners to keep on mining to ensure the security of the network. Also, every transaction carries a fee that destroys coins in the process, making them unavailable for circulation allowing miners to continue mining for block rewards.
Nobody knows how it'll all work out in the end, but the idea is to have people make use the coin often enough to have a ton of transactions/fees, enough transactions/fees that destroy coins and allowing the miners to keep receiving block rewards given them enough incentive to continue to ensure the security of the network; but if this is to work the coin has to reach mainstream adoption allowing more and more people to use the coin in order to destroy enough coins through fees to keep the miners mining.
1,000,000,000,000 (Trillion) Doge
The max dogecoin is not a trillion, it's 100 billion (100,000,000,000), or was this an attempt at being witty?