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Question for you: What do you mean by "work with?"
That is, do you intend that these other persons will be passive investors, active partners, or employees?
You may want to consider giving the 5% partners economic rights to profits but no management rights. This is typical in an LLC. You could add the right to repurchase their respective interests for the equitable value of their investment at the time of repurchase. That way, if things don't work out, you buy them out and say goodbye.
Their liability would be limited to their investment (unless they commit some act that is outside the scope of the business, in which case, it would be their problem and not the LLC's -- or, at least that's the theory). In practice, however, having active partners who have no management responsibility argues STRONGLY for liability insurance, to protect the management owners from being held liable for the stupidity (pardon me, for the errors and ommissions) of their non-mangement partners, who assert to third parties that they have management powers.
You have to draft an operating agreement that sets forth the various provisions for the operation of the LLC; including adding, transferring and terminating memberships, and the various classes of ownership.
Then the original partners vote to add a member and then issue an agreement whereby the new member obtains X% of ownership in consideration for whatever the new member is providing as consideration (usually money, but not always). Everybody signs and you're on board.
You also have to register the LLC with the CA Secretary of State.
Lots of online services will provide fill-in-the-blanks LLC agreements and registrations ($). The only way you will get a custom agreement is to have an attorney draft it ($$$$).
I am still confused as to which type of an agreement (what is it's name?) are we going to issue? Can we limit the new member's rights and voting priviliges when it comes to making decisions for the LLC?
The agreement is called an "operating agreement." It's the document under which an LLC operates (thus the name of the agreement).
An example of an operating agreement can be found here: http://business.uschamber.com/tools/opagree_m.asp.
However, this is a Delaware LLC, so it may not be entirely applicable to California.
No, I mean that you could reference the operating agreement in an agreement between existing members and new members.
But, you could amend an existing operating agreement, instead.
There's no "one" right way to do it.
It's commonly called a "buy-sell" agreement.
Is my answer acceptable?
Yes, that will work.
I have no suggestion in this area. Sorry.
You're welcome and good luck.