We had DAI three and a half years after DA2, and that was working with a whole new engine. Aside from this "one game per year" rule, why would it take five years for a new DA title? Do we even have any indication what the new IP is, let alone that it'll launch in 2018?
We should keep in mind that release dates aren't necessarily 100% influenced by the actual development of the game, or when they're ready to be released. EA's financial outlook factors into it too. I remember that was one of the reasons given for DA2 being so rushed; it had to launch in a certain quarter to make the earnings results look better. So as odd as it sounds, the "one game per year" thing can actually be a significant consideration for the publisher when it's working out what will ship, and when.
I don't really think DA4 would take five years (so, like, late 2019?) but Andromeda is in 2017, and the new IP has to launch some time - it's been in development since at least September 2012. Andromeda will definitely come first, then I expect the new IP, then DA4.
They might try to launch Andromeda in Feb/March 2017 and the new IP in November or December, which would leave 2018 open for DA4. At this point everyone is just speculating.