Here are some ways a team could lose 5 yards: You call more time outs than you have, false start, there are more than 11 players on the field from a team, a free kick is too short, a forward lateral pass occurs, or if a free kick goes out of bounds. There are plenty more ways to lose 5 yards. 

A loss of 15 yards happens when: clipping occurs, a fair catch interference occurs, unnecessary roughness occurs, roughing the kicker occurs, tripping occurs, or when there are non-players on the field.

A loss of half the distance to the goal line occurs when: a pass interference occurs by the defense in the endzone with the ball originally beginning the down within one yard of the endzone, or when the distance to be assessed by a penalty is greater than the distance to either goal line

Loss of the ball occurs when: there is an interference with a fair catch which is also a 15 yard penalty, when the offense fails to cover enough yards to make the first down, or when the kicking team first touches the ball except in a kickoff.