Answer
See answer below
Work Step by Step
Let $r$ be scarlar and let $v=\{v_1,v_2,v_3,v_4,v_4\}$ and $w=(w_1,w_2,w_3,w_4,w_5\}$ be vectors in $R^5$
We obtain:
$r(v+w)=r[(v_1,v_2,v_3,v_4,v_5)+(w_1,w_2,w_3,w_4,w_5)]\\
=r(v_1+w_1,v_2+w_2,v_3+w_3,v_4+w_4,v_5+w_5)\\
= [r(v_1+w_1),r(v_2+w_2),r(v_3+w_3),r(v_4+w_4),r(v_5+w_5)]\\
=(rv_1+rw_1,rv_2+rw_2,rv_3+rw_3,rv_4+rw_4,rv_5+rw_5)\\
=(rv_1+rv_2+rv_3+rv_4+rv_5)+(rw_1+rw_2+rw_3+rw_4+rw_5)\\
=rv+rw$
