While I agree extended warranties are usually just rip offs, you don't have a 5/6 year warranty for an item under sale of goods you have the 5/6 year period from the time you realised their was a fault to do something about it, and the longer it is the less likely it is you will get a refund or exchange you will have to fight for it the law doesn't just entitle you to a refund/exchange within 5/6 years you may have to accept a partial refund or credit.
People buy extended warranties to hopefully make it easy to get refunded replaced without courts or lots of hassle with no guaranteed outcome.
No you have a non defined period of time to make a claim up to 6 years. What you have described only applies in Scotland where you have 5 years from the point of discovery to make a claim.
The sale of goods act is not a warranty it is your basic legal rights which in most cases cover you more than most extended or manufacturer warranty's.
There is no legal requirement for a company to provide any type of warranty but they have to for-fill the requirements of the law which is the sale of goods act. Anything added by a company whether paid for or not is always in addition to your statuary rights.