Half of the ten table
Ten sevens are seventy, so five sevens are thirty-five. That is the whole table in one sentence, and it is quicker than any of the chanting. It also explains the ending: halving a number that ends in a nought gives 5 or 0, never anything else.
It is already in the room
A clock face is the 5 table. The 4 is at twenty minutes because 5 × 4 = 20, and a child who reads the clock has been using this table for a year without calling it one. Pointing that out is usually worth more than another round of practice.
Where it goes wrong
Almost nowhere, which is exactly why it is worth doing early. The 5 table is the table that makes a child believe they can learn the tables, and that belief is the thing that gets them through the 7 and the 8.