To simplify the expression $(5a^5 - a^4) + (a^5 + 7a^4 - 2)$, we need to combine like terms.

First, distribute and combine the terms:

• The $a^5$ terms: $5a^5 + a^5 = 6a^5$
• The $a^4$ terms: $-a^4 + 7a^4 = 6a^4$
• The constant term: $-2$ remains as is, since there are no other constant terms to combine with it.

Putting it all together, the simplified expression is:

$6a^5 + 6a^4 - 2$