I am having cataract surgery. My optometrist told me my multifocal lens implant will cost me $5000 per eye and I have to pay before. Is this correct?

Prices vary. Multifocal lenses do cost extra and are not covered by health insurance. They are not mandatory but can be very helpful if you are trying to achieve independence from glasses. The price is a combination of surgeon fees and the cost of the lens. The price is dependent on the market in the area and is variable. There's nothing wrong with price shopping. Just make sure you go with a great surgeon..
Yes but. Multifocal lens implants can work very well in the right patient. They are not covered by insurance and do represent an out-of-pocket cost to the patient. This cost varies and is determined between the patient and his/her doctor. $5000 per eye extra is definitely on the high side of the spectrum. You should discuss with your surgeon directly.
Excessive! Sounds excessive. 2-3 times the typical cost. You need to be educated on thees types of lenses and make sure it is what you want and need to meet your expectations first. You may be very satisfied with a standard monofocal intra-ocular lens and making both eyes for distance (you will need readers to read), or mono vision with a near eye and distance eye. If you were not informed, go elsewhere!
This is high. This is roughly twice the price that this service typically costs (at least in kentucky). You should shop around. Also it is unusual for a 40 year old to need cataract surgery. You should get a second opinion to see if you really need the surgery.
Insurance coverage. Major insurance carriers (aside from a flexible spending account) do not cover multifocal (MIOL) or any premium intraocular lenses for cataract surgery. They only cover monofocal (corrects usually only distance VA or reading or intermediate: not all 3 like MIOLs can in general). Depending on other technology used (Laser femtosecond laser, ORA, limbal relaxing incisions, etc), $3000-6000 per eye.