Grayish Under Eye Lines After Restylane

It's difficult to imagine that what you are seeing is related to the Restylane injections if it has been over 5 years. There is a side effect of Restylane injections called the Tyndall effect whereby Restylane that is injected too superficially (near the surface of the skin) can cause a bluish hue. But in cases where this effect is present, it normally wears off within about 9 months for the area under the eyes.
We are wondering if you still have swelling as you mention it, but then focus on the gray line. If swelling or lumpiness is still present, then hyaluronidase is certainly an option, but one that we are not sure would have any effect based on the amount of time that has passed. We recommend getting a second opinion from another experienced dermatologist or plastic surgeon. Good luck.

Greyish-blue discoloration under the skin can be seen after injection of HA fillers. This is due to a refraction of light by the particles, known in physics an the Tyndall effect. It is due to the implant being too close to the skin surface. Since the eyelid skin is so thin, it commonly is seen in this area. I have found that it takes a very long time for these areas to go away by themselves.
Sometimes I use a large-bore needle to puncture the skin over the collection of HA and can literally squeeze it out. This immediately improves the blue discoloration. Because the eyelid skin is so thin, I have had trouble using this technique in the lower lid area. I would recommend using hyaluronidase. An injection will resolve the discoloration overnight.

Although I suppose it is possible, if restylane was injected very superficially it has been known to hang around for a year or more.  But 4 years after ...I do not think so?

Under eye Restylane injections can last a long time. It is certainly not impossible that it could last over a year. However, it would be unusual for the Restylane to be present after 5 years. As a first step I would try some Hyaluronidase injections, just in case some of the product is still present.
If that does not work, it is possible that you have a problem called post inflammatory hyperpigmentation. Some people (usually those with more pigmented skin) tend to deposit pigment into their skin after there is any irritation in the area. This is particularly likely to happen if you get sun exposure while the skin is irritated soon after the injection, or if you had a significant bruise from the treatment.
There are excellent prescription medications to reverse this type of abnormal pigment deposits. One of the most effective combinations is Hydroquinone and Retin-A. However, there are other possibilities as well.
I would discuss this with your dermatologist or cosmetic surgeon to see if a prescription cream may help your problem.