Oh boy, it would suck to only have five. But, here goes!
First and foremost is Apollyon. I don't love this devilsaur because he's rare, or because he was an epic tame, or because of his notoriety. I love him because he had a personality before I even tamed him. In my eyes, he was conceited, hot-headed, egotistical, and stubborn. I had to prove to him that I was worth fighting alongside. Then, and only then, would the King of Sholazar join me. But for all his "flawed" personality traits, he harbors a deep love and respect for my hunter (that of course is mutual), and I love that about him.
Next is Tetsusaiga. Honestly it was a tough choice between him and Apollyon for first. Reason he's second is because somewhere along the way, I made the foolish decision to release him. This cat was my first real, honest, "epic" tame. I tamed him just mere months after the game launched. Plenty of people had cats of one sort or another, but I had never seen anyone with Echeyakee. He was a Horde-only quest mob, and back then, it wasn't quite as easy or common for someone to get a pet like that. It was his appearance (saw him right here on Petopia) that first drew me to him, and then when I discovered how unique he'd be on the Alliance, I had to have him. A very generous undead fellow summoned the cat when he saw me waiting there (was waiting on my brother to get the quest, he had made a Horde character to help me), and /cheered me on when I got him. I'll never forget that guy (though I don't remember his name or class), and I'll never forget Tetsusaiga. I only hope I can get him back now, and that it's not too late to reunite with my "first love".
Third is Vulkoor. The bronze Madexx was my first tamed, and while I liked him, I just didn't click with him at all. I decided I was going to park my butt in Uldum as long as I had to in order to get green Madexx. I don't even remember how long I was there. One day, during what I was expecting to be a very long camp, this black Madexx appeared behind me after about 3.5 hours. I meant to give him to a friend, but couldn't find her, and I ended up basically accidentally taming him (long story). Annoyed, I threw him in my stable and continued about my camp for green. A few days later, another friend got a bronze Madexx with my other friend and her green Madexx in the area. We decided to take some pictures of all three of us and our Madexxes. Since my friend had a bronze, I didn't want to bring my bronze too, so I brought black. But while we were taking pictures, my black one really started to grow on me. It was so unexpected and rather sudden. I felt that this black one, though he wasn't my "dream" Madexx, belonged to me, and I to him. Now I don't care if I see 50 green Madexxes, I don't want them. Vulkoor is my dream scorpid, though I didn't realize it the time, because my obsession with having a matching pet almost made me miss one of the best tames to happen to me.
Naphthali is next up. It was during a raid break in ICC that I noticed a beautiful spider critter with this color. I was so impressed with its beauty that I decided I'd try to find a tamable one. I had tried spiders in the past, but only tarantulas, and never clicked with them. I honestly didn't expect my next spider to be any different. I found a rare, Naraxis, of this color, and made for Duskwood. When I arrived, it wasn't there, so I went to the next closest location, Zul'Gurub. After some embarrassingly fail pulls on my part (been a while since I raided there and forgot about the "drunk" effect and all the humanoids and such), I managed to barely snag one of these, and named her Naphthali which means "struggling". She immediately took on a protective, motherly personality, yet also somewhat naive and sweet at the same time. Still, I intended to get the rare to replace her (I like rares). Went to Naraxis' cave one night and sure enough, it was up. But I didn't just release Naphthali. I set her to "Stay" at the entrance of the cave just to go take a closer look at Naraxis. I couldn't do it. I looked back at Naphthali, sitting there all sweet and loyal as always, and I realized that rare or not, I couldn't let this girl go. Turns out now, that the Razzashi Broodwidows have been retired, making my girl more rare than a "rare".
Last, but not least, is my dear friend Sheldon. He's been through some color changes (this one having the most "Sheldon"-like feel to it), and took a vacation from my stables for a time, but he's never lost the connection with me. This turtle is dependable beyond dependable. While we haven't done anything incredibly epic together, he's saved my butt more times than I'd like to admit, and he's just so adorable. I love him in this form so much, that even though I think Terrorpene looks amazing, I can't have any other turtle than Sheldon, and I won't "change" him to the new model. Sheldon is Sheldon, and he's staying just as he is.
While I have a few other "favorites", they didn't make the cut because they lack that certain "something", that spark that regardless of the passage of time or circumstances, I can't imagine my stable without them. While Naphthali is pretty terrible to solo-quest with (she's soooo squishy), I refuse to let her go. While Vulkoor is enjoying his time in the spotlight as my tanking pet, Sheldon will always be there, steadfast as ever. I love my Shikon (Gondria), Ysuran (green carrion bird), and the others that were near the top of my list, but they are just missing that something.
Somehow I managed to narrow it down to 5. These would be my choices:
Granted, if I do find Karoma, and none of my friends who want to tame the beauty are online, I may just tame her and name her after my best in-game friend (her main being a shaman). But, then I wouldn't be able to freak people out with my Cheshire Bear...
or 
