Between them Anish, Jason and Rob have 40 swap cards. Jason has twice as many as Anish, and Rob has five times as many as Anish.

How many does Anish have?

Let's assume Anish has x swap cards.

Jason has twice as many as Anish, so Jason has 2x swap cards.
Rob has five times as many as Anish, so Rob has 5x swap cards.
The total number of swap cards is x + 2x + 5x = 40.
Combining like terms, we get 8x = 40.
Dividing both sides by 8, we get x = 5.
Therefore, Anish has 5 swap cards. Answer: \boxed{5}.

Let's assign variables to each person's number of swap cards:

Anish: A
Jason: J
Rob: R

Given that Jason has twice as many swap cards as Anish, we can write the equation J = 2A.

Also given that Rob has five times as many swap cards as Anish, we can write the equation R = 5A.

We are also given that the total number of swap cards among them is 40, so we can write the equation A + J + R = 40.

Using the information above, we can solve for Anish's number of swap cards (A):

Substituting the value of J from the first equation into the third equation, we have:
A + 2A + R = 40
3A + R = 40

Substituting the value of R from the second equation into the equation above, we have:
3A + 5A = 40
8A = 40
A = 40 / 8
A = 5

Therefore, Anish has 5 swap cards.