5. Calculate the sum of all the products listed in the table:

| $2004 \cdot 2006$ | $2004 \cdot 2007$ | $2004 \cdot 2008$ | $2004 \cdot 2009$ |
| :--- | :--- | :--- | :--- |
| $2005 \cdot 2006$ | $2005 \cdot 2007$ | $2005 \cdot 2008$ | $2005 \cdot 2009$ |
| $2006 \cdot 2006$ | $2006 \cdot 2007$ | $2006 \cdot 2008$ | $2006 \cdot 2009$ |
| $2007 \cdot 2006$ | $2007 \cdot 2007$ | $2007 \cdot 2008$ | $2007 \cdot 2009$ |
| $2008 \cdot 2006$ | $2008 \cdot 2007$ | $2008 \cdot 2008$ | $2008 \cdot 2009$ |
| $2009 \cdot 2006$ | $2009 \cdot 2007$ | $2009 \cdot 2008$ | $2009 \cdot 2009$ |

Each task is scored with 10 points.

The use of a pocket calculator or any reference materials is not allowed.
5. If we sequentially extract the numbers 2004, 2005, 2006, 2007, 2008, 2009 in rows, we get:

$$
\begin{aligned}
& 2004 \cdot(2006+2007+2008+2009)=2004 \cdot 8030 \\
& 2005 \cdot(2006+2007+2008+2009)=2005 \cdot 8030 \\
& 2006 \cdot(2006+2007+2008+2009)=2006 \cdot 8030 \\
& 2007 \cdot(2006+2007+2008+2009)=2007 \cdot 8030 \\
& 2008 \cdot(2006+2007+2008+2009)=2008 \cdot 8030 \\
& 2009 \cdot(2006+2007+2008+2009)=2009 \cdot 8030
\end{aligned}
$$

Now let's sum the rows. If we factor out the number 8030, we get that the desired sum is equal to

$$
8030 \cdot(2004+2005+2006+2007+2008+2009)=8030 \cdot 12039=96673170
$$