ACTIVISTS in Hong Kong, Taiwan and overseas Chinese communities are mapping out joint plans to mark the fifth anniversary of the Tiananmen Square crackdown on June 4. Sources in the dissident community said commemorative events would also be held in various Chinese cities even though mainland police were pulling out all stops to keep them under control. The activists will call on the Beijing authorities to release prisoners of conscience, to overturn the verdict on June 4, to penalise those responsible for the armed suppression of the student movement, to end the one-party dictatorship and to build up ademocratic China. Events in the United States, home of the largest number of exiled dissidents, will be co-ordinated by the United Front for Democracy in China. A gathering will be held in San Francisco on the occasion of the unveiling of a statue similar to the ''Goddess of Democracy'' erected in Tiananmen Square in May 1989. Speakers will include astrophysicist Fang Lizhi and leaders of the student movement Wu'er Kaixi and Liang Er. Li Lu, one of the ''commanders'' of the demonstrators in the square, will host a large-scale commemorative function in New York. Exiled students and intellectuals in American cities, including Los Angeles and Washington, are also expected to observe the anniversary. Locally, the Hong Kong Alliance in Support of the Patriotic Democratic Movement in China plans to host a variety of activities in addition to its annual rally and candle-light vigil in Victoria Park. Two films - Li Lu's Moving the Mountain and Escaping from China by Tiananmen Square leader Zhang Boli - are scheduled to be shown. There will be taped messages from overseas dissidents and those who have returned to China. Other functions include ''democratic kite-flying'' and laying wreaths during the Ching Ming Festival. Other cities where commemorative activities have been planned include Taipei, London, Paris, Sydney and Toronto. Sources in Beijing said security officials were trying to block links between the dissident community and their supporters overseas.