Answer
$21$ ways
Work Step by Step
You have 7 articles and only have time to read 5 of them,order does not matter so this is a combination problem.
There are $7$ choices and $5$ will be chosen so use the formula $_nC_r=\dfrac{n!}{(!(n-r)!}$ to obtain:
$_7C_5=\dfrac{7!}{5!(7-5)!}$
$_7C_5=\dfrac{7!}{5!(2!)}$
$_7C_5=\dfrac{7 {\times}6{\times} 5 {\times} 4 {\times} 3 {\times} 2 {\times} 1}{(5 {\times} 4{\times}3{\times}2 {\times} 1)(2{\times}1)}$
$\require{cancel}
_7C_5=\dfrac{7 {\times}6{\times} \cancel{5 {\times} 4 {\times} 3 {\times} 2 {\times} 1}}{\cancel{(5 {\times} 4{\times}3{\times}2 {\times} 1)}(2{\times}1)}$
Simplify to get
$_7C_5=21$
There are $21$ ways.
