The top-voted answer on Do I really need to replace my helmet every 2-3 years if it hasn't been in a crash? (not the accepted answer), points to the "Bicycle Helmet Safety Institute" which suggests that your helmet would still be usable:
In sum, we don't find the case for replacing a helmet that meets the ASTM or Snell standards that compelling if the helmet is still in good shape and fits you well.
Another source of advice that's independent of manufacturers, Consumer Reports largely concurs:
The Consumer Product Safety Commission, for example, advises that unless manufacturers recommend otherwise, you should get a new helmet every five to 10 years. The Snell Foundation, a standard-setting body that’s known to be one of the strictest in terms of helmet safety, says that normal wear-and-tear is enough to recommend helmet replacement every five years or so, though this is a judgment call, and wouldn’t apply, for example, to an unused helmet stored in good condition.
(emphasis mine)
Unless the helmet has been stored in a way that would expose it to regular UV, or a continuous presence of solvents, and as long as there are no obvious defects (crumbling foam, cracked shell) then it seems reasonable to assume it would be safe to use.
Note that, since the last time this question was asked, research papers published in 2016 and 2017 have investigated this question and found no meaningful degradation even in 20-year-old helmets.
Foam cores were extracted from 63 used and unused bicycle helmets from ten different models spanning an age range of 2–20 yrs. All cores were impact tested at a bulk strain rate of 195s−1. Six dependent variables were determined [...] Age did not affect any of the dependent variables; however, greater foam density, which varied from 58 to 100 kg/m3, generated significant increases in all of the dependent variables except for yield strain.
"Age Does Not Affect the Material Properties of Expanded Polystyrene Liners in Field-Used Bicycle Helmets", Journal of Biomechanical Engineering, April 2016
Helmets (n = 770) spanning 0–26 years old were drop tested to measure peak linear headform acceleration during impacts to the right and left front regions of the helmets at two impact speeds (3.0 and 6.2 m/s). [...] Overall, age was related to either no difference or a statistically significant but small increase (≤0.76 g/year of helmet age) in peak headform acceleration. Extrapolated across 20 years, age-related differences were less than both style- (traditional vs. BMX) and size-related differences.
"Age has a Minimal Effect on the Impact Performance of Field-Used Bicycle Helmets", Annals of Biomechanical Engineering, May 2017
This second, larger, study tested donated used helmets as long as they had no impact damage, so it's a decent baseline for an intact, reasonably maintained helmet.
