To solve this equation, we can start by simplifying the fractions:

(x + 5)/2005 + (x + 6)/2004 + (x + 7)/2003 = -3

To find a common denominator, we can multiply each fraction by the product of the denominators:

2004*2003*((x + 5)/2005) + 2005*2003*((x + 6)/2004) + 2005*2004*((x + 7)/2003) = -3*2004*2005

Simplifying further:

2004*2003*(x + 5) + 2005*2003*(x + 6) + 2005*2004*(x + 7) = -3*2004*2005

Expanding:

2004*2003*x + 2004*2003*5 + 2005*2003*x + 2005*2003*6 + 2005*2004*x + 2005*2004*7 = -3*2004*2005

Combining like terms:

2004*2003*x + 2005*2003*x + 2005*2004*x + 2004*2003*5 + 2005*2003*6 + 2005*2004*7 = -3*2004*2005

Simplifying further:

x(2004*2003 + 2005*2003 + 2005*2004) + 2004*2003*5 + 2005*2003*6 + 2005*2004*7 = -3*2004*2005

Combining like terms:

x(2004*2003 + 2005*2003 + 2005*2004) + 2004*2003*5 + 2005*2003*6 + 2005*2004*7 = -3*2004*2005

Simplifying further:

x(2004*2003 + 2005*2003 + 2005*2004) + 10020*2003 + 12030*2004 + 14035*2005 = -3*2004*2005

Expanding:

x(4012023124 + 4014025155) + 20060160 + 24096120 + 28140775 = -6012061200

Simplifying further:

x(8026048279) + 72297055 = -6012061200

Multiplying:

8026048279x + 72297055 = -6012061200

Subtracting 72297055 from both sides:

8026048279x = -6084358255

Dividing by 8026048279:

x = -6084358255/8026048279

Therefore, the solution to the equation is x = -6084358255/8026048279.