Representative Bill Flores of Texas said he would not seek re-election in 2020, joining a long list of Republicans retiring in a state that has become increasingly competitive.

“When I originally announced that I was running for Congress in 2009, I was firm in my commitment that I would run for six or fewer terms,” Mr. Flores, who is serving a fifth term, said in a statement on Wednesday. “After much prayer over the past few days and following conversations with my wife, Gina, during that time, I have decided that my current term will be my last.”

With his announcement, Mr. Flores became the fifth Republican in the state to bow out of the next election cycle, rather than face challengers. Representative Will Hurd, the only black Republican in the House, and Representatives Michael Conaway, Pete Olson and Kenny Marchant also recently announced they did not plan to run again.

Texas Republicans, who have enjoyed a generation of dominance, are facing resistance as the population diversifies and because of their connection to President Trump and his incendiary brand of nationalist politics, including from suburban voters, a once dependable base.