Number of ways $4$ digit numbers can be formed from the digits $1,2,3,4,5,6,7$ will be $(\color{purple}{\text{without repetition}})$
= $\color{violet}{840 \hspace{0.1cm} ways}$
Now, the number should be divisible by $5$
$\color{chocolate}{\text{Divisibility Rule of 5 says that }}- \color{maroon}{\text{The last digit of the number should be}}$ $\color{red}{0}$ $\color{maroon}{or}$ $\color{red}{5}$
∴ We'll fix $5$ at the unit place
Remaining digits can be arranged in
= $\color{pink}{120 \hspace{0.1cm} ways}$
∴ $\color{red}{120} \color{green}{\text{ 4 digit numbers can be formed from the digits 1,2,3,4,5,6 and 7}}$
$\color{green}{\text{which are divisible by 5 when none of the digits are repeated}}$