Context. PKS 1510-089 is one of only a few flat spectrum radio quasars detected in the very-high-energy (VHE, > 100 GeV) gamma-ray band. Aims. We study the broadband spectral and temporal properties of the PKS 1510-089 emission during a high gamma-ray state. Methods. We performed VHE gamma-ray observations of PKS 1510-089 with the Major Atmospheric Gamma Imaging Cherenkov (MAGIC) telescopes during a long, high gamma-ray state in May 2015. In order to perform broadband modeling of the source, we have also gathered contemporaneous multiwavelength data in radio, IR, optical photometry and polarization, UV, X-ray, and GeV gamma-ray ranges. We construct a broadband spectral energy distribution (SED) in two periods, selected according to VHE gamma-ray state. Results. PKS 1510-089 was detected by MAGIC during a few day-long observations performed in the middle of a long, high optical and gamma-ray state, showing for the first time a significant VHE gamma-ray variability. Similarly to the optical and gamma-ray high state of the source detected in 2012, it was accompanied by a rotation of the optical polarization angle and the emission of a new jet component observed in radio. However, owing to large uncertainty on the knot separation time, the association with the VHE gamma-ray emission cannot be firmly established. The spectral shape in the VHE band during the flare is similar to those obtained during previous measurements of the source. The observed flux variability sets constraints for the first time on the size of the region from which VHE gamma rays are emitted. We model the broadband SED in the framework of the external Compton scenario and discuss the possible emission site in view of multiwavelength data and alternative emission models.