Geometry of the pentachloridoindate(III) anion
TL;DR Initially published crystal structure of $\ce{[NEt4]2[InCl5]}$ [1] according to the further investigations [3], is not valid. The $\ce{InCl5^2-}$ ion does not have $C_\mathrm{4v}$ symmetry, and VSEPR theory pretty much explains formation of numerous slightly distorted trigonal bipyramidal $\ce{InCl5^2-}$-containing complexes according to the most recent single-crystal structure experiments. 

From the other side, the bond lengths and geometry index refer to the dominating character of square pyramidal environment, which is in this case can be dictated by the crystal packing, towards which $\ce{[InCl5]^2-}$ is more sensible than $\ce{[SnCl5]-}$ due to the noticeable size difference ($\ce{[InCl5]^2-}$ is bulkier). Either way, it looks like another crystallographic experiment (preferably at lower temperatures to decrease the size of thermal ellipsoids) is needed to determine the angles more precisely. 

As a general advice, always pay attention to the $R_1$ and $R_2$ values of the crystal structure. A rule of thumb: a good structure refinement of small molecules should lead to $R_1 &lt; 0.05$ and $R_2 &lt; 0.12$.



Crystal structure of $\ce{[NEt4]2[InCl5]}$, determined in 1969 [1], has been subsequently criticized in several publications, mainly involving additional symmetry vibration analysis of Raman spectra for $\ce{MX5^2-}$ anions [2]. It's been established that $\ce{InCl5^2-}$ ion does not have $C_\mathrm{4v}$ symmetry (but retains $C_\mathrm{2v}$), and that the crystal may not be centrosymmetric. 

The results are summarized in [3]:




  Deconvolution of the single-crystal data was again performed with the aid 
  of the low temperature data, revealing $11$ $\ce{InCl5^2-}$ bands between $300$ and $\pu{100 cm-1}$. Two overlapping A stretches are clearly evident at $292$ and $\pu{286 cm-1}$, but no B stretch is apparent. The two E symmetry stretches expected for the anion of a $C_2$ site, but not for a $C_4$ site, are evident at $281$ and $\pu{271 cm-1}$. [...] With the aid of low-temperature data, the four E modes predicted for $\ce{InCl5^2-}$ at $C_2$ sites are found at $144$, $136$, $122$, and $\pu{103 cm-1}$ in the single-crystal data. With this reinterpretation of the spectrum it is no longer necessary to assume arbitrarily the presence of a lattice mode in this region.
  
  In summary, the vibrational data for the tetraethylammonium salts of $\ce{InCl5^2-}$ and $\ce{TlCl5^2-}$ indicate that these complexes reside on sites lacking full $C_4$ symmetry. The most straightforward conclusion from the vibrational data is that the $\ce{InCl5^2-}$ ions have local $C_2$ symmetry, which would be inconsistent with the previous structure determination [1]. [...] 
  
  The structure of $\ce{[(C2H5)4N]2[InCl5]}$, as previously reported, consisted of centrosymmetrically related $\ce{InCl5^2-}$ ions situated about the 
  Wyckoff c positions of $C_4$ symmetry in space group $C_\mathrm{4h}-P4/n$. 
  Coaxial with the $\ce{InCl5^2-}$ ions are disordered $\ce{(C2H5)4N+}$ ions 
  also situated about the Wyckoff c positions. The N atoms of the two remaining $\ce{(C2H5)4N+}$ ions in the unit cell occupy the centrosymmetrically related Wyckoff b sites of $S_4$ symmetry, the cation as a whole again being disordered. There are two disturbing features of this solution and its subsequent refinement: the disorder of the $\ce{(C2H5)4N+}$ ions and the significant residual electron density in the region of the basal Cl atoms of the tetragonal-pyramidal anion.


It is demonstrated further that for the ordered model the most satisfying crystallographic interpretation coexists with $C_2$ rather than $C_4$ symmetry. A correlation of allowed point symmetries implies switching from $P4/n$ to $P\bar{4}$ space group, thus reducing $R$-factor ($R_1$) from $9.5\%$ to $6.7\%$. 


  During the refinement in $P\bar{4}$, small but significant changes 
  occur in the basal plane of the $\ce{InCl5^2-}$ ion. The basal Cl atoms 
  have moved by $\pu{-0.5 A}$ from their fourfold symmetric positions in $P4/n$, leading to variations in the bond distances and angles about the In atom (Figure 3) that are qualitatively sufficient to explain the vibrational results.


 

Geometry index $\tau_5$ for $\ce{[InCl5]}$ fragment can be used to determine formal coordination environment as follows:

$$\tau_5 = \frac{\beta - \alpha}{60^\circ},$$

where $\alpha$, $\beta$ - two greatest valence angles of the coordination center ($\angle \ce{Cl - In - Cl}$, $\alpha &lt; \beta$).

\begin{align}
\begin{cases}
\tau_5 &amp;= 0 \qquad &amp;\text{square pyramidal geometry} \\
\tau_5 &amp;= 1 \qquad &amp;\text{trigonal bipyramidal geometry}
\end{cases}
\end{align}

For the original $\ce{[NEt4]2[InCl5]}$ structure refined in [3] I've taken angular values from their supplementary materials. It turned out that changing space group to $P\bar{4}$ still results in dominating character of square pyramidal geometry of $\ce{[InCl5]^2-}$, though one must remember that the rotation axis of highest order is $C_2$, not $C_4$: 

$$\alpha = (150.6 \pm 5.0)^\circ, \beta = (154.1 \pm 6.0)^\circ, \bar{\tau_5} = \frac{154.1^\circ - 150.6^\circ}{60^\circ} = 0.06; \tau_5 \in [0.04; 0.24]$$

Paper [4] mentions that for isoelectronic $\ce{[SnCl5]-}$-contining structures with various cations only trigonal-bipyramidal geometries were reported, and suggests higher influence of crystal packing on $\ce{[InCl5]^2-}$ geometry. This can also be explained by higher flexibility of $\ce{MX5}$ fragment in $\ce{[PPh4]2[InCl5]}$ in comparison with $\ce{[PPh4][SnCl5]}$ [5] due to greater average bond length: $d(\ce{In - Cl}) = \pu{2.5 A}$, $d(\ce{Sn - Cl}) = \pu{2.3 A}$.

As for auxiliary experimental data, all crystal structures including $\ce{[InCl5]^2-}$ fragment determined in the past two decade completely support VSEPR theory that predicts trigonal bipyramidal $D_\mathrm{3h}$ symmetry (with one intermediate exception of $\tau_5 \approx 50\%$). 




bis(Tetraphenylphosphonium) pentachloro-indate(III) [4], trigonal bipyramidal geometry:
$$\alpha = 124.24^\circ, \beta = 174.74^\circ, \tau_5 = \frac{174.74^\circ - 124.24^\circ}{60^\circ} = 0.84$$

$\color{#EEEEEE}{\Large\bullet}~\ce{H}$;
$\color{#909090}{\Large\bullet}~\ce{C}$;
$\color{#FF8000}{\Large\bullet}~\ce{P}$;
$\color{#1FF01F}{\Large\bullet}~\ce{Cl}$;
$\color{#A67573}{\Large\bullet}~\ce{In}$.







bis(Diphenyldichlorophosphonium) pentachloro-indate(III) [6], trigonal bipyramidal geometry:
$$\alpha = 120.93^\circ, \beta = 179.29^\circ, \tau_5 = \frac{179.29^\circ - 120.93^\circ}{60^\circ} = 0.97$$

$\color{#EEEEEE}{\Large\bullet}~\ce{H}$;
$\color{#909090}{\Large\bullet}~\ce{C}$;
$\color{#FF8000}{\Large\bullet}~\ce{P}$;
$\color{#1FF01F}{\Large\bullet}~\ce{Cl}$;
$\color{#A67573}{\Large\bullet}~\ce{In}$.







tetrakis($\mu_3$-Selenido)-tetrakis($\mu_2$-1,5-bis(diphenylphosphino)pentane)-deca-gold(I) pentachloro-indate(III) [7], intermediate geometry:
$$\alpha = 138.45^\circ, \beta = 166.50^\circ, \tau_5 = \frac{166.50^\circ - 138.45^\circ}{60^\circ} = 0.47$$

$\color{#EEEEEE}{\Large\bullet}~\ce{H}$;
$\color{#909090}{\Large\bullet}~\ce{C}$;
$\color{#FF8000}{\Large\bullet}~\ce{P}$;
$\color{#1FF01F}{\Large\bullet}~\ce{Cl}$;
$\color{#FFA100}{\Large\bullet}~\ce{Se}$;
$\color{#A67573}{\Large\bullet}~\ce{In}$;
$\color{#FFD123}{\Large\bullet}~\ce{Au}$.







tetrakis($\mu_2$-chloro)-chloro-tetrakis(triphenylphosphine-P)-di-copper(I)-indium(III) tetrahydrofuran solvate [8], trigonal bipyramidal geometry (though authors refer to it as to "quasi square-pyramidal" coordination based on a single slightly shorter $\ce{In - Cl}$ bond distance $(d(\ce{In-Cl_\mathrm{ap}}) = \pu{2.36 A})$, shortest $d(\ce{In-Cl_\mathrm{eq}}) = \pu{2.42 A})$: 
$$\alpha = 123.90^\circ, \beta = 172.89^\circ, \tau_5 = \frac{172.89^\circ - 123.90^\circ}{60^\circ} = 0.82$$

$\color{#EEEEEE}{\Large\bullet}~\ce{H}$;
$\color{#909090}{\Large\bullet}~\ce{C}$;
$\color{#FF8000}{\Large\bullet}~\ce{P}$;
$\color{#1FF01F}{\Large\bullet}~\ce{Cl}$;
$\color{#C88033}{\Large\bullet}~\ce{Cu}$;
$\color{#A67573}{\Large\bullet}~\ce{In}$.






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