One of the charms, or frustrations (depending on your disposition) of the Myst games, is that you don't really have a clue what you're doing when you start. Explore and enjoy the environment, and take good note of all the details. For example, try to open doors, look for objects you can pick up, watch for special symbols. As you go along, some things will become clearer (and others won't ).
Try to keep an open mind, be curious, and investigate everything you see.
I hope you'll enjoy Myst V! It's wonderful to play a Myst game for the first time!
I recommend playing the first Myst if you haven't already done so, since it is one of the simpler games and it would also bring you some backround information. Ir is also a great idea to play Myst 2:Riven and Myst 4:Revelation, as they are the more succesful ones(in my opinion) and pertain the most to the story of a main character. Uru is also a great game, and seems to be the most related to Myst5, even though i didnt really enjoy it.
The Myst series as Vogelaar said so well, are games of mystery. Even in the first Myst, you are immediately launched into this world with no idea of your purpose or how you got there. You have to explore and solve puzlles and slowly find out at least dimly your task, (although Myst 3:Exile tells you almost exactly in the beginning) and then usually there is a choice to be made at the end of the game which will determine your succes(although all the different endings are fun to play!)
The world of Myst is easy to immerse yourself in and i hope you enjoy it!
On the game to start with - I have a different recommendation. I love Myst, it's my favorite game of all time, but I don't recommend that you start with it. It's an older static game, and it looks dated, even the 3D version of Myst, realMyst. I recommend that you start with the game you want to play - in your case that would be Myst V.
Yes, wander around, take notes, and click on things. I'd also recommend that, if you never played a game like this, start with a walkthough. There are several excellent walkthroughs listed in the following thread in our forum - a stickied thread (!) at the top of this section of the forum - Myst V hints and walkthroughs
You don't have to use the whole walkthrough - just use enough to get yourself started. Solve a puzzle or two, using the walkthrough, to get a feel on how the game works, and the steps you take to solve the puzzles and uncover the story. All the walkthrough's are great, though I'm rather partial to Bert Jamin's walkthrough myself.
Also, be sure to "save, save, save", as I said in another stickied thread. In Myst V, taking a picture with the in-game camera creates a game save. There's a bug where you may find yourself getting further along in the game than you should be, based on the puzzles you solved. It's a real disconnect - you end up bypassing sections of the game where Esher talks to you, and so you don't learn the whole game story. If this happens to you, you may want to revert to a previous save.