Accepted answer
Five days at minus 80 °C. minus 80 °C is 85 kelvin below a refrigerator, and below the glass transition of a lyophilised cake the ten-degree rule of thumb stops applying at all — solid-state chemistry is not slow liquid chemistry, it is a different regime, and the failure modes that survive it are mechanical rather than chemical. The thing to establish is how many times it froze and thawed, not how long it sat: five days at one stable temperature is gentler than a single uncontrolled transition. Either way, record the five days and the temperature now, while you still know them; an excursion you did not write down is an excursion you cannot interpret later.
The honest answer is that the cold pack is doing much less than people think and that shipping lyophilised is what actually protects the material.
Arrhenius behaviour means the degradation rate roughly doubles per ten degrees. A week at thirty degrees is therefore a meaningful exposure for a solution and an immaterial one for a dry solid.
Worth being precise here: a pack that arrived hard tells you about the last day of transit only, since it will have melted and, if the ambient dropped, partially refrozen.
Single-use temperature loggers are standard practice in supply chains where temperature genuinely matters and are inexpensive at parcel scale.
Solutions are a different question and deserve the worry the solids get.