Work backwards from Stop 5 to Stop 1. Let $x$ be the number of passengers picked up at Stop 1.

After Stop 5, there are $13$ passengers. At Stop 5, half were dropped off, so before Stop 5 there were:

$13 \times 2 = 26 \text{ passengers}$

At Stop 4, $11$ passengers were picked up, so before Stop 4 there were:

$26 - 11 = 15 \text{ passengers}$

At Stop 3, half were dropped off, so before Stop 3 there were:

$15 \times 2 = 30 \text{ passengers}$

At Stop 2, $3$ passengers were picked up, so before Stop 2 there were:

$30 - 3 = 27 \text{ passengers}$

Since the bus had $0$ passengers before Stop 1, the number picked up at Stop 1 is:

$x = 27$