Let be a very ample line bundle on a smooth complex projective variety of dimension . We classify the polarized manifolds such that there exists a smooth member of endowed with a branched covering of degree five . The cases of and are already studied by Lanteri-Palleschi-Sommese.
"Projective manifolds with hyperplane sections being five-sheeted covers of projective space." J. Math. Soc. Japan 58 (4) 1119 - 1131, October, 2006. https://doi.org/10.2969/jmsj/1179759539