Given my predilections, it shouldn't be surprising that for the most part, I'm going to lean towards post punk New Wave, especially stuff that has a drum machine and a synthesizer as the main instruments. But not exclusively.
In no particular order (and if you ask me again next month, there may be some significant differences in my choices. Maybe.)
"Bizarre Love Triangle" by New Order.
I've included the official music video version, but for years, the version (and only version) that I had was the 12" one that's included on Substance. In the meantime, I've come to also really love the Richard X remix. It's a little tough to leave off "Blue Monday" but I think I should only have one song per band or artist when I'm only picking five songs anyway, and I do like "Bizarre Love Triangle" better. And, as an aside, when I first met my wife, we danced to "True Faith." I like both of the other mentioned songs better than that one, though. Sorry, hon.
"If You Leave" by Orchestral Manoeuvres in the Dark
You can probably see why I tend to just write OMD; that British spelling of maneuvers is killing me. Every single time I write it.
I don't actually really like the movie Pretty in Pink all that much, but for whatever reason, OMD's "If You Leave" definitely makes the cut of one of the top songs of the decade at me. Never featured on any album other than the soundtrack for the movie and OMD's various greatest hits compilations is kind of a real shame; you have to go a little bit out of your way to pick this one up (along with their other great song, "Dreaming".) For what it's worth, this song also makes my teen-aged daughter's list, but she is a big fan of Pretty in Pink. In fact, she watches the movie on Netflix every couple of months or so.
"Behind the Wheel" by Depeche Mode
It's hard to pick a single Depeche Mode song. I think that Music for the Masses is my favorite album of theirs, though (although that's a hard pick), and of the songs on that album, certainly "Behind the Wheel" is my favorite. I think "Enjoy the Silence" is the single most iconic DM song ever, and probably their single best single, but it was not released in the 80s (5 February 1990) and more properly belongs, of course, along with the rest of Violator with the transition into 90s post-New Wave Alternative music.
I've included the album version rather than the single version, which was remixed and which misses out on a lot of the dark droning menace of the album version, honestly. There's also a very interesting Vince Clark remix of the song that came out much more recently.
"A Little Respect" by Erasure
To show that I'm not all dark and edgy with my synthesizer New Wave music, I should probably put something like Erasure on the list too (although I'm also tempted by Book of Love and Pet Shop Boys for this slot.) And among Erasure's songs, is it "A Little Respect" or "Oh, L'amour" that gets the nod? I'm going with the former just because The Innocents was the first Erasure CD I picked up and I have some nostalgic attachments to it above and beyond the others for that reason alone. There's a great 12" for "A Little Respect" including an Extended Mix and a Big Train Remix. The 12" Vocal and Dub remixes, on the other hand, are not worth the trouble.
"Animal" by Def Leppard
Not everything that I listen to and like is synthesizer New Wave from the second half of the decade, though. As we get to the "bottom" of the top five, I'm finding more and more that there is a ton of material competing to be on the list. But, hard choices have to be made! Duran Duran gets edged out, as does a-ha, Real Life, and a bunch of other similar artists. In fact, I think that I definitely need representation from at least one of the "hair rock" bands of the 80s. For this selection, I went with my favorite track from Hysteria, which is truly one of the greatest albums of all time. Competition for the glam metal bands was pretty fierce, though--strong output from guys like Quiet Riot, Whitesnake, Mötley Crüe, Van Halen, Ratt and more merited consideration. At the end of the day, there could only be one, however, and "Animal" gets the nod.