Aims. We examined the physical properties of molecular clouds (morphology, column density, number density, mass) to investigate the mechanism of triggered star formation by UV radiation from a massive star.Methods. We made extensive, high-resolution maps of molecular clouds associated and interacting with the W5-East H ii region using the 45-m telescope at the Nobeyama Radio Observatory (HPBW = 15. 6) in 13 CO (J = 1−0) and C 18 O (J = 1−0) to reveal details in the high-density regions of the molecular clouds. In addition, to investigate the spatial distributions of young stellar objects (YSOs) in the W5-East H ii region, we mapped the spatial distributions of Class I and II candidates.Results. We identified eight 13 CO molecular clouds (three of them are known bright-rimmed clouds) and nine C 18 O clumps. The masses of the clouds and clumps range from 460 to 36 000 M and from 55 to 740 M , respectively. The peak 13 CO column densities of the clouds facing the H ii region are twice as large as the others. They have steep density gradients toward the H ii region, indicating interactions with the H ii region. We selected 55 Class I candidates and 778 Class II candidates associated with the W5-East H ii region from the previous Spitzer IRAC/MIPS survey. Most Class I candidates are located around integrated intensity peaks of 13 CO, whereas most Class II candidates are distributed along the front sides of the BRC arcs close to the exciting star. Conclusions. The alignments of the YSO candidates and the molecular clouds in order of age indicate that triggered star formation occurs in the W5-East H ii region as a result of gas compression by strong UV radiation. Based on the column densities of 13 CO and the spatial distribution of YSO candidates, we identified a new bright-rimmed cloud candidate on the west side of the W5-East H ii region.