The reason for this is:
1st Inning: Getting through the jitters of throwing the first couple pitches of the game can make or break the entire game for many. Not being prepared mentally will create rough waters and tough times getting into the flow of the game. Preparation starts from the bullpen you throw 2-3 days before the game. A small part of preparation on game day starts with a routine of warming up, throwing program, and finding rhythm/tempo and timing in the bullpen.
5th Inning: This is the second toughest inning for starting pitchers because it is the inning that must be completed to get the win. This thought enters into many pitchers heads subconsciously. Being tough mentally by being able to stay in the moment, one pitch at a time, is what it takes to accomplish what each pitcher sets out to do each game. Win!
Last Inning: The last inning is the 3rd toughest inning in a game that many would say is the most difficult! The hitters awareness is heightened due to it being his last at bat of the game. Every hitter wants to finish his last at bat with a positive result and many times bares down mentally tougher than any other at bat during the game. Each pitch is crucial. This is why Closers are paid so much to only pitch 1 inning at the end of each close game. If a starting pitcher is still in the game, he is probably around his pitch limit or wearing down physically. Mental and physical toughness comes into play at this point in the game and those that prepare in every way will find themselves in this position more often than others.