Price of some item has decreased by $5\%$. Then price increased by $40\%$ and now it is $1352.06\$$ cheaper than doubled original price. How much did the item originally cost?
1. Let the original price of the item be \( x \).

2. The price decreased by \( 5\% \), so the new price after the decrease is:
   \[
   x - 0.05x = 0.95x
   \]

3. The price then increased by \( 40\% \), so the new price after the increase is:
   \[
   0.95x + 0.40 \cdot 0.95x = 0.95x \cdot (1 + 0.40) = 0.95x \cdot 1.40 = 1.33x
   \]

4. According to the problem, this new price is \( 1352.06 \) dollars cheaper than double the original price. Therefore, we can set up the equation:
   \[
   1.33x = 2x - 1352.06
   \]

5. Solving for \( x \):
   \[
   1.33x = 2x - 1352.06
   \]
   \[
   2x - 1.33x = 1352.06
   \]
   \[
   0.67x = 1352.06
   \]
   \[
   x = \frac{1352.06}{0.67}
   \]
   \[
   x = 2018
   \]

The final answer is \( \boxed{2018} \)