Final Fantasy V is my absolute favorite Final Fantasy games. If you are still confused to any degree, here are some unique points/information about the first five Final Fantasy games to help clarify:
Final Fantasy 1 features a very generic plot about 4 light warriors who must relight the 4 elemental orbs by defeating 4 elemental fiends, and then confront a further evil power which has been building behind the scenes. At the start of FF1 you choose the classes of your party, and there is no change in this (other than leveling up/buying spells/equipment) until they upgrade to essentially better versions of the same classes. FF1 was for the Famicom/NES and later remade for the Wonderswan Color (WSC), and that version was enhanced/rereleased in Final Fantasy Origins (PSX) and Final Fantasy: Dawn of Souls (GBA).
Final Fantasy II has a more complex storyline about a group of orphaned siblings fighting an empire; there are four in the beginning but one is lost and you begin the game with only three of the characters. These characters are all flexible in their abilities, but have natural built-in tendancies and skills to a certain degree. FF2 was for the Famicom and later remade for the WSC; that version was later enhanced and featured in Final Fantasy Origins (PSX) and Final Fantasy: Dawn of Souls (GBA), which were both released in the US.
Final Fantasy III backtracked to FF1 in some ways with four generic characters who can be set to certain classes and must blahblah 4 elemental crystals blahblah evil and learn the history of the creation of the world and three powerful individuals in it, one of whom is the primary villain of the story- mostly- and two of whom will more or less aid the light warriors in their quest. However, this game introduced some new concepts; it introduced the class change system, allowing characters to change to one of a set of classes (with more becoming available later in the game); it featured four different airships, each with unique differences and limitations; and it was incredibly long and featured multiple overworlds. FF3 was for the Famicom/NES and has since been rereleased on the WSC; it hasn't been released in the US but will be soon in a new remake for the Nintendo DS. The NES ROM has been translated for a long time though.
Final Fantasy IV featured a very set storyline and very set characters; it was a very complex story about mysterious corruption suddenly appearing in the world and various people's response to events, and seemingly someone who was attempting to take over the world- though there's more at work in the background than that. It was unique in that it allowed for five characters in the party, followed a very linear design, and thus was extremely straightforward. The characters in the party left and returned a lot. FFIV was for the SFC/SNES and released as "Final Fantasy II" in the US; it was remade for the WSC, ported to "Final Fantasy Chronicles" for the PSX (which contained FF4 and Chrono Trigger... making the name a strange choice), and has recently been rereleased/enhanced to some degree for the Gameboy Advance.
Final Fantasy V returned heavily to Final Fantasy III's pattern and did it one better. It featured kind of a lofty, often silly plot which feels sort of like an anime series of some kind, but still revolved around the old concept of four elemental crystals and four warriors (and four other warriors...). The character change system was brought back and made far more complex, with the ability to learn permanent skills by training in a class, then use those skills in a different class; and further, classes you mastered training in would give you some permanent benefits if you returned to being an unclassed character. Unclassed characters are also allowed to use more skills than classed characters, and will inherit a lot of automatic benefits from their mastered classes... so you can see where this becomes a very strongly personalized system where you can mix and match and build very powerful characters. However, the game was on a pretty good difficulty spike too, so while you might become "godlike" it wasn't something you could do by accident. FFV was for the SNES/Famicom and not released in the US; it was later ported to Final Fantasy Anthology for the PSX (which is a somewhat rare game), and is now being released for the GBA. Apparently the GBA has new classes and dungeons, too... oh, and I NEED a copy. That is all.
As for later Final Fantasy games: VI is extremely well known, released as III for the SNES and ported in Final Fantasy Anthology, and is kind of a mix of FFII and FFIV's designs (very flexible characters in a very complex storyline, who come and go a bit); VII everyone and their dog but me seems to think is utterly badass, and is for the PSX and PC, and to be honest I've never gotten very far in it; VIII, IX, X, XI, and XII I know pretty much nothing about. FFX2 looks interesting, and the words "class change system" help. I'll play the newer games someday...
Oh, and by the way, the fighter class of FF1, FF3, "Frionel" in FF2 (well, the NES version; remakes sport a weird guy who looks more like Locke), the knight class in FF3, Cecil in FF4 (later in the game; initially he wears dark knight armor), and Butz/Bartz in FF5 all have the exact same hairdo and very similar posture.