Level 5 troops give 7% mana bonus. This means that by only having this, an average mana hero will be charged in 10/ 1,07 = 9,35 tiles.
There are two ways doing it. The one I do it (Kind of backward) or you can multiply the # of tiles with the mana bonus and see when it passes 10. So, 9 * 1,07 = 9,63 which is how you do it.
Your calculation is also correct. Mine shows that you would need 9,35 tiles sent at the target to charge up with only a level 5 mana troop, yours show that you will charge as 9,63 tiles when 9 tiles are fired. Both show that 9 tiles will not charge the hero with level 5 mana troop.
If you continue your calculation and end up with 9 * 1,12 = 10,08 you will see that a level 5 mana troop (7%) and full costume bonus (5%) is enough for it to reduce to 9 tiles. Same 10/1,12 = 8,93.