No way, you're asking for trouble. Are you really going to be able to control 4 kids running in different directions, wanting to go on different rides, some hungry now, some hungry later, some needing to use the restroom now, others refusing, but 10 minutes later, beg for the restroom? And what happens if you somehow lose a kid? Do you really want the liability of losing one kid in the park, even if for just 15 minutes, then for the kid to tell their parent he was lost for "one hour" (kids exaggerate), and he was so scared? I wouldn't trust ANYONE who is not in my family to care for my child in a large place like an amusement park when they have their hands already full so if my child were one of your guests, I'd politely decline, unless I also receive permission to come along.
Of course, I would never expect people to pay my way. I have always offered to pay my way even when it was something as minor and inexpensive as going to watch a movie. Better safe than sorry, and I'd rather come off as being too generous than being a cheapskate who wants others to pay her way and her child's. I realize the invitation is for my child, not for me and my child. Now if you want to go ahead and pay for a parent as well, that is at your discretion, but unless the invitation is addressed to "Sammy and mom", then I would assume only Sammy is being paid for, not me, as the mommy, as well. If you feel most people would assume they are being paid for, then add a disclaimer, or something like "drop-off requested." I assume parents will call about that, and say they are not comfortable doing so. At that time, you can offer them to come along, but at their own expense, as you don't have the budget to pay for 4 other parents.
My suggestion is this: you can have a Lego themed party at a park, get a Lego cake, Lego decor, hand out Legos, have games involving building things out of Legos, contests to see who can make the coolest thing out of Legos, or who can make something the fastest, etc., but save the amusement park visit for family. Assuming the kids were older, I might feel differently, like a pre-teen or teen group being dropped off would be fine, but at this age, kids get tired, cranky, stubborn, and most parents will feel uncomfortable dropping off their young child with someone who has their hands full and is in such a large place that a child could easily get lost. Maybe I am just overprotective, but the comments below seem to agree with that thought -- that 5 is too young for a "drop-off" situation.