Answer
$1, 2,7,32,157,...$
Work Step by Step
Given: $a_{n}=1,a_{(n+1)}=5a_{n}-3$
$a_{1}=1$
$a_{(2)}=5a_{1}-3=5(1)-3=2$
$a_{(3)}=5a_{2}-3=5(2)-3=7$
$a_{(4)}=5a_{3}-3=5(7)-3=32$
$a_{(5)}=5a_{4}-3=5(32)-3=157$
Hence we see that the first five terms are $1, 2,7,32,157$
