We measured the pressure dependence of in-plane resistivity $rho_{ab}$ in the recently-discovered iron-based superconductor Ca$_{10}$(Ir$_{4}$As$_{8}$)(Fe$_{2-x}$Ir$_{x}$As$_{2}$)$_{5}$, which shows a unique structural phase transition in the absence of magnetic ordering, with a superconducting transition temperature $T_{rm c}$ = 16 K and structural phase transition temperature $T_{rm s}$ $simeq$ 100 K at ambient pressure. $T_{rm c}$ and $T_{rm s}$ are suppressed on applying pressure and disappear at approximately 0.5 GPa, suggesting a relationship between superconductivity and structure. Ca$_{10}$(Ir$_{4}$As$_{8}$)(Fe$_{2-x}$Ir$_{x}$As$_{2}$)$_{5}$ is a rather rare example in which the superconductivity appears only in a low-temperature ordered phase. The fact that the change in the crystal structure is directly linked with superconductivity suggests that the crystal structure as well as magnetism are important factors governing superconductivity in iron pnictides.
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