In measure 5 of the example the distance between the alto and soprano notes is a sixth--F-sharp up to D. The three sixths in measure 5 do not move--they repeat. The right hand alone can easily play sixths that do not move.
However, at the beginning of measure 6 the soprano and alto parts move in parallel motion: the soprano moves down a step from D to C-sharp as the alto also moves down a step from F-sharp to E (yellow highlights). This is difficult for the right hand to execute alone, especially in a lively tempo or when the parallel motion continues further in the same direction. Substitution and much stretching would be required, both of which are especially difficult for those with small hands.
The left hand is not very active at that moment, and its tenor notes are near the alto notes. This sets the stage for redistribution of the inner (alto) part between the hands.