Answer
See answer below
Work Step by Step
Let $r$ and $s$ be scarlars and let $v=\{v_1,v_2,v_3,v_4,v_4\}$ be a vector in $R^5$
We obtain:
$(r+s)v=(r+s)(v_1,v_2,v_3,v_4,v_5)\\
=[(r+s)v_1,(r+s)v_2,(r+s)v_3,(r+s)v_4,(r_s)v_5]\\
=(rv_1+sv_1,rv_2+sv_2,rv_3+sv_3,rv_4+sv_4,rv_5+sv_5)\\
=(rv_1+rv_2+rv_3+rv_4+rv_5)+(sv_1+sv_2+sv_3+sv_4+sv_5) \\
= rv+sv$
