To find the first difference between the second term \(3a + 5\) and the third term \(8a - 3\), we subtract the second term from the third term:
First difference = Third term - Second term
\[ = (8a - 3) - (3a + 5) \]
Now, simplify this:
\[ = 8a - 3 - 3a - 5 \]
Combining like terms:
\[ = (8a - 3a) + (-3 - 5) \] \[ = 5a - 8 \]
Therefore, the first difference is:
\[ \boxed{5a - 8} \]