Is an operation necessary for a herniated lumbar disc of 5cm?

Second Opinion. I suspect that you meant 5 millimeters, not centimeters. The need for surgery is dependent on many things. Are you having neurologic problems such as weakness, numbness or pain. Is the condition something that you can resolve with nsaids, rest, massage, and so forth. If in any doubt discuss this with a different surgeon than the one who is suggesting surgery. Hope this helps and good luck.
No. Like my colleagues, the size is 5 mm? Back surgery is a serious event, and should be considered if: uncontrollable pain, with progressive weakness, atrophy, numbness, and interference with ambulation. If there is bladder dysfunction, no longer room for hesitation, as surgery is vital. These are my generic guidelines, but all patients are different. If you wait the disc may dry out and shrink.
Depends. If there is neurologic deficit or severe pain surgery could be considered. This you need to decide together with a surgeon. There are no straight answer.