Sir Robert Salusbury Cotton, 5th Baronet (c. 1739 – 24 August 1809) was an English politician. He was Member of Parliament (MP) for Cheshire from 1780 to 1796.
Son of Sir Lynch Cotton, he was one of the founders of the Tarporley Hunt Club in 1762. In 1774 he was elected a fellow of the Royal Society.
Educated at Cambridge, soon after the birth of his second son he moved from the old Salusbury seat at Lleweni Hall to Combermere Abbey, the traditional seat of the heir apparent to the Baronetcy. The subsequent leasing of the family's former estate to the Hon Thomas FitzMaurice, a brother of Lord Shelburne's, was necessitated by the profligacy of his uncle, Sir Thomas. Nevertheless, Sir Robert kept a large hunting establishment and was known as a generous host.
He married Frances Stapleton, daughter and co-heiress of James Russel-Stapleton Esq in 1767. In 1774 they were visited at Llewenli Hall by Sir Robert's cousin, Hester Thrale, who was accompanied by the noted writer, Samuel Johnson; Frances "found Johnson, despite his rudeness, at times delightful, having a manner peculiar to himself in relating anecdotes that could not fail to attract old and young. Her impression was that Mrs. Thrale was very vexatious in wishing to engross all his attention, which annoyed him much". The Cottons later broke off relations with Hester following her 1784 marriage to an Italian music teacher.
Sir Robert and his wife had the following children: