To simplify the expression \( 5(a - 3b) - 4a + b \), we start by distributing \( 5 \) in the term \( 5(a - 3b) \):
\[ 5(a - 3b) = 5a - 15b \]
Now, we can rewrite the entire expression:
\[ 5(a - 3b) - 4a + b = (5a - 15b) - 4a + b \]
Now, combine the like terms for \( a \):
\[ 5a - 4a = 1a \quad \text{or simply} \quad a \]
Next, combine the like terms for \( b \):
\[ -15b + b = -15b + 1b = -14b \]
Putting it all together, we have:
\[ a - 14b \]
Therefore, the expression \( 5(a - 3b) - 4a + b \) simplifies to \( a - 14b \).
The answer is \( \boxed{B} \).