They are taking the government to the European Court of Human Rights in a bid to end the system of male primogeniture which has resulted in almost all titles being passed to male heirs, the BBC reported.
The five women, who are part of the Daughters' Rights campaign, want the UK government to remove the word "male" from legislation they describe as "outdated" so they can stand for by-elections to the Lords.
The group accuse the government of "double standards" because it promotes women's rights.
The five women involved in the case are: Lady Willa Franks, eldest daughter of the Earl of Balfour; Lady Eliza Dundas, eldest daughter of the Earl of Ronaldshay; Sarah Long, elder sister to the current Viscount Long of Wraxall; Tanya Field, eldest daughter of the Earl of Macclesfield, and Hatta Byng, eldest daughter of Viscount Torrington.
Under the principle of male primogeniture, sons, nephews and uncles take precedence over daughters, nieces and aunts when a title is passed on to the next generation.
While some hereditary titles can be inherited by women because of the rules surrounding the way they were originally created, all but one of 92 current hereditary peers are male.
The Daughters' Rights campaign says the system breaches Article 14 of the European Convention on Human Rights, when taken alongside Article 3 of the First Protocol, the right to a free election.
In 2013 the Equality (Titles) Bill was introduced in the Lords with a view to allowing for equal succession of female heirs to hereditary titles and peerages but it was voted down.
UK courts do not have oversight over the rules governing parliamentary procedure, the BBC report said.
Solicitor Paul Hardy, from law firm DLA Piper which is bringing the case, said the application to the European Court of Human Rights "raises profound questions about sexual equality and membership of the House of Lords".
The barrister for the campaign, Edward Legard, said: "It seems wrong in a country where women, including now royal women, are born with equal opportunities, that we continue to discriminate against one group based only on gender.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)