Let's simplify the given expression step by step:

(a/5 + a + 5 + a/5 - a) / (3a + 5/a + 5)
= (a/5 + a + a/5) / (3a + 5/a + 5)
= (2a/5 + 2a) / (3a + 5/a + 5)
= 2a(1/5 + 1) / (3a + 5/a + 5)
= 2a(1/5 + 5/5) / (3a + 5/a + 5)
= 2a(6/5) / (3a + 5/a + 5)
= 12a/5 / (3a + 5/a + 5)
= (12a) / (5(3a) + 5 + 5)
= 12a / (15a + 10)
= 12a / 5(3a + 2)
= 12a / 5(3a + 2)

Therefore, the simplified expression is 12a / 5(3a + 2).