Is the 5d orbital involved in triiodide ion?
Professor Klüfers presents a structure of the $\ce{I3-}$ ion in his general and inorganic chemistry introductory course at the LMU Munich. The ion is linear and the $\ce{I\bond{...}I}$ distances are identical, measured experimentally to be $293~\mathrm{pm}$.

In neutral iodine, the $\ce{I-I}$ distance is measured to be $272~\mathrm{pm}$.

We see a notable increase in bond length which indicates a decrease in bond order. A reduction of bond order — say from a bond order of $1$ (single bond) to one of $0.5$ (four-electron three-centre bond) — means that we cannot add an additional bonding orbital to the mixture. Otherwise we would have something along the lines of two single bonds (bond order $1$), which is how the ‘octet expansion’ traditionally was explained.

The reduction in bond order is best explained — as mentioned — by a four-electron three-centre bond and thus without d-orbital participation.