The brother of President Hassan Rouhani of Iran was sentenced to five years in prison on corruption charges, the state news media reported on Tuesday, and four people were sentenced in another case on charges of spying for the United States and Britain, with one person facing the death penalty.

The penalties added to the perception that Mr. Rouhani is under increasing pressure in Iran, where he won elections in 2013 and 2017 partly on promises to curb corruption and end the country’s prolonged economic isolation.

Instead, corruption has flourished, the landmark 2015 nuclear agreement promoted by Mr. Rouhani is near collapse, and Iran’s economy has been seriously hurt by President Trump’s restoration of sanctions.

Mr. Rouhani’s brother, Hossein Fereydoun, was arrested in 2017 in connection with long-running accusations of corruption, and the Iranian judiciary said at the time that he was the subject of “multiple investigations.”