WASHINGTON—A former Trump campaign aide previously indicted by special counsel Robert Mueller pleaded guilty Friday to two charges, making him the fifth person to publicly admit to criminal misconduct, and the third Trump associate to cooperate, in the wide-ranging probe into alleged Russian meddling in the 2016 election.

The plea by Richard Gates, a former campaign aide to President Donald Trump, adds to pressure on his longtime business associate and former Trump campaign chairman Paul Manafort, who, with Mr. Gates, pleaded...