Beware of where the moon is too! Shoot away from it if it's up. Also, take the opportunity to include the landscape in the shot(or composite) with the moon light. It will be cool!

My galaxy photos are similar to others.... 14mm lens, ISO 1600, f/2.8, 40 seconds.
You will still need to process them a bit. You can also take a dark frame to "subtract" the noise (same exposure as the real image except you leave the lens cap on. Some cameras have a long-exposure noise reduction mode which causes the camera to internally take a dark frame immediately following the real shot (e.g. if I enable this on my camera and take a 40 second shot, the camera will actually take 80 seconds. It'll take 40 seconds with the shutter open, followed by 40 more seconds with the shutter closed. That means I don't need to pop on a lens cap, but that's a trivial thing to do if your camera doesn't have a noise reduction mode.)
Milky Way by Tim Campbell1, on Flickr
BTW, the above was taken in "good" but not "great" dark skies. You can see the glow of light pollution above the trees which you don't see at the very top of the image. I was having difficulty with this. At a darker sky, ISO 3200 would have worked better, but at this location it just picked up even more light pollution. I had to really work on this in post to improve the contrast. Also the best months to take such an image would be in July or August when Sagittarius is up (that's probably the brightest part of the Milky Way with the best structure of dust lanes, etc.)
This was taken in September and Sagittarius had already set -- so this is not the richest part of the Milky Way. Knowing "when" to get the best image is as much as knowing the best exposure to use.
While using mirror lockup will not hurt, it won't make any positive difference either. Think about it: if you need a long exposure to burn a dark scene onto the sensor, how much light do you think will enter the sensor in the fraction of the second that the mirror will be moving if you don't lock it up?I highly recommend using the wireless remote with mirror lock up. Let the internal timer run out from mirror up to picture actuation. I've been doing that with my astrophotography and it helps with vibration reduction.
Five seconds at f/2.8 would require an insanely-high ISO that would show more noise than stars (unless you're shooting with a Nikon D4). See Tim's comment below for solid information.Shooting that wide you should be able to get away with 5" exposure @ 2.8 without any streaks and adjust ISO as needed. The wider you go the more play you have with exposure time.
I agree with all of the above, except maybe the use of the camera's noise reduction (unless you don't mind waiting for about 30 seconds between photos). At the settings Tim suggested, expect your ISO not to have to go higher than 1600. The below is not necessarily a well-composed photo, and the aurora kind of "ruined" the night sky by making it brighter, but it shows you what you can get at f/2.8, 30 seconds, ISO 1600.The wider you are shooting the longer exposure you can do. I believe a good formula for calculating the maximum time without showing star trails is 600/Focal Length(35mm equivalent). So the tokina at 11mm is going to be 16.5mm equivalent on a 1.5x sensor. 600/16.5 = ~36sec. So to be safe I would stick to 30second exposures to minimize the formation of star trails. You are going to want to shoot wide open, high ISO, and focused to infinity with noise reduction on if you have it. If you are shooting a foreground with the milky way you are going to want to shoot 2 frames with 2 different focus points. Make sure you are using a steady tripod. If you dont have a remote shutter release I would set the timer and expose for 30sec. Dont worry to much about the high ISO.
Why not also recommend shooting the Milky Way using flash? It won't do any harm either, so why not?Meh. 1stly, I use remote with mirror lock up on a telescope mostly but also with night shots as well and I don't see why you couldn't use it doing landscape shots such as yours posted above. Doesn't hurt anything to use it, does it? 2ndly, Tim said the same thing I said which was my point: The wider you are shooting the longer exposure you can do.
Why not also recommend shooting the Milky Way using flash? It won't do any harm either, so why not?
I haven't shot with a telescope before, but I assume that having the ability to magnify the stars should also bring more light in, which means that locking up the mirror might make a difference in that case. But, unlike what you just said, shooting the sky with a telescope and shooting a nocturnal landscape at 11mm are actually totally different beasts.
I have no interest in engaging in a pointless discussion but someone needs to point out when certain advice is not good. I'm not a night-shooting expert by any means, but I know enough to realize that you shouldn't be dishing out advice – let alone using "meh" when your expertise is put into question with the facts. Yes, the wider you are shooting the longer the exposure you can do, but the best the OP can do is completely ignore everything you wrote, to avoid confusion.
The fact is that it doesn't hurt to use remote + mirror lock up with a long focal length or short focal length with night time exposures. If you think there is harm in that advice it is your problem.
...so it's safe to say that you have reading-comprehension issues. I won't bother replying to the rest of your good stuff.While using mirror lockup will not hurt, it won't make any positive difference either.