Solve for value when expr is a list

Another possibility is to convert your list into a logical expression:

bool = Or @@ Thread[{t-5, t+2} == 0]

Solve[bool, t]

-5 + t == 0 || 2 + t == 0

{{t -> 5}, {t -> -2}}

What you are asking can be done, but it's not the expected form for Solve.

Using Map (/@), Thread and Function (#&)

First[Solve[#, t]] & /@ Thread[{t - 5, t + 2} == 0]

{{t -> 5}, {t -> -2}}