Let x be the number of oranges in the first basket.

The number of oranges in the second basket is 640 - x, as together they have 640 oranges.

Now, it is given that one-fifth (1/5) of the oranges in the first basket are taken to the second basket. This means (1/5)x oranges are moved to the second basket.

After this transfer, the number of oranges in the first basket becomes x - (1/5)x = (4/5)x.

The number of oranges in the second basket becomes 640 - x + (1/5)x = 640 - (4/5)x.

Now, according to the problem, when the number of oranges in both baskets becomes equal, we can set up an equation:

(4/5)x = 640 - (4/5)x

To solve for x, first, let's get rid of the fractions by multiplying both sides of the equation by 5:

4x = 3200 - 4x

Now, add 4x to both sides of the equation:

4x + 4x = 3200

8x = 3200

Next, divide both sides by 8 to solve for x:

x = 3200 / 8

x = 400

So, there were 400 oranges in the first basket.