I'll echo others sentiments of that program. It's deceptive in it's simplicity, yet when you employ it with a solid work ethic, and enough food, you will grow.
There are several aspects of this program that many would dismiss, until they have really looked at it and understand what they are seeing. As BTB said, you don't just jump into this type of program at a run. You need to allow some time for your conditioning to allow an all out assault. Even with good conditioning, you can overreach your abilities, and need a break for recovery.
The Park 5x5 is my preferred method of progression. I generally use either a fullbody or an A/B split as my template to work from. I tend to prefer the A/B over the fullbody at this time.
There are a couple of ways to gauge when to add weight with the Park 5x5. I have in the past gone up in reps till I was completing 5x8, and then increased weight. Or, you could go with a smaller increase when you have hit 5x5, and just microload with 2.5 lbs plates.
I would advise, especially when starting out, go up in reps to 8, and then add weight. Make small weight increases in the beginning, no more than 5lbs, and then start back at 5 reps, and work your back up. There's a few reasons to do this, but I don't have time right now to go into it.