Action Comics takes place roughly six years ago too, doesn't it? I don't really think this contradicts anything, as its still within reason that the public tagged Arthur with the name "The Aquaman" after the jeans and t-shirt wearing Superman took to the streets and had already been so named.
I, frankly, don't care that they have this '5 year timeline', I've 'retconned' it to 12 years ago (and even then it's tight). The 'five years' point is the 'superhero boom'.
12 years ago: Batman starts (he's around 20); 'Superboy' is a 'country legend' (he's around 15)
11.5 years ago: Death of the Graysons
11 years ago: Dick is recruited (he's 11) (still not comfortable with his age being so close to Kal's, though, or the 'small' gap between him and Bruce); Bruce and Talia tango (this is either when Damien was conceived or when the mingled genetic material was obtained...)
7 years ago: Superman goes public; Jason begins training
6 years and 4 months ago: Superman saves Metropolis from The Collector
6 years and 3 months ago: Clark Kent joins The Daily Planet
6 years ago: Aquaman is revealed; Dick is now Nightwing and Jason is Robin (The Anti-Superman Army steals the engine of Kal's ship); Kal investigates the rumours of 'The Batman'
5 years and 5 months ago: Barry becomes The Flash; Aquaman and The Others team up; Aquaman rescues Oliver Queen
5 years and 2 months ago: Diana comes to Man's World and Hal becomes Earth's Green Lantern; Barry and Hal meet and encounter Grodd
5 years ago: JLA is formed, Batman is no longer an 'urban legend' and Darkseid is defeated (oh, and Vic becomes 'Cyborg')
4.5 years ago: J'onn joins the JLA
4 years ago: Jason dies; J'onn 'tests' the JLA and finds them lacking; Barbara becomes Batgirl; Lois discovers The Secret
3.5 years ago: Tim is recruited (Bruce isn't keen on this)
3 years ago: Tim is Robin; Barbara is shot
2.5 years ago: Jason returns
2 years ago: Damien seeks out Bruce
1.8 years ago: Superman 'dies'
1.5 years ago: Bruce 'dies' and Dick becomes Batman
1 year ago: Superman returns (this one is hard to place as the indications are that it's relatively recent but also that he only recently returned to Metropolis..and we don't yet know where he had been, so it may be that he came back from the dead and then left Metropolis for a while)
0.5 years ago: Bruce returns and starts up Inc; split with Tim
Couple of months ago: Superboy awakes; Tim is behind 'NuWikiLeaks'; Batman encounters No-Man; Damien kills No-Man; Joker has his face removed
1 month ago: New Daily Planet building is unveiled, 'alien attack' in Metropolis; Superboy hunts down the Teens; JLA fights Amazo; Green Arrow tries to join the JLA
A few weeks ago: second 'alien attack'; Superboy 'escapes'; Green Arrow is still trying to join the JLA; Batman is in the Labyrinth
A couple of weeks ago: Batman escapes, punches Dick; Court of Owls attacks Gotham, JLA lend a hand and Green Arrow is still trying to join them
Over the course of the past week: Kara lands on Earth, is attacked, attacks Kal, finds out Krypton is gone, is lured into a trap, exposed to Kryptonite, escapes, destroys a multi-billion dollar satellite and unwittingly leaves some of her blood behind, finds Argo, encounters Reign, is left for dead, returns to Earth and saves it from a team of (incompetent) Worldkillers, attacked by humans, meets Siobhan, flees with her, goes to a bar and 'meets' Siobhan's dad (insert parts yet untold); Superman is 'replaced' and starts exercising a firm hand on Metropolis; Kara spots Superboy, talks to him and then smacks him around a little, tells him he's going to be a killer, heads to Metropolis, catches McCoy and encounters doppleganger of Kal-El, gets smacked around, is saved by the real Kal-El (insert parts yet untold)
A day ago: Clark agrees to pick up Lucy from the station on Lois' behalf and that Jimmy can stay at his place for a while, ends up tangoing with Helspont and getting in Lucy's bad book
Dr Sivana starts his hunt
I've left out the JLI and JLD stuff and it seems the Captain Ma...Shazam stuff hasn't happened yet as it's not yet Christmas...
Oh, and Knightfall (I'm not sure if that's still in continuity)