When pattern changes...?

In cell F2, enter the formula

=IF(OR(B1<>B2,C1<>C2,D1<>D2,E1<>E2),ROW(),"")

and copy down to match column E.

Then format G2 as a date, and use the formula

=IFERROR(INDEX(A:A,MATCH(SMALL(F:F,ROW(A1)),F:F,FALSE)),"")

and copy down to match column F, or until you get blanks.

This uses basically the same logic but a slightly different approach:
To get the dates for the transitions, the values in the columns are mated vertically. When they don't match, then the next "set" is started and the date is noted.
This formula will see the difference in the "sets" and bring the date to column F using OFFSET to get the date from column A. Format column F for dates and enter this in F2 and fill down:

Formula:

=IF(OR(B1<>B2,C1<>C2,D1<>D2,E1<>E2),OFFSET(F2,0,-5,1,1),"")

The dates are now in column F. To condense this column of dates, format column G as dates and enter this array formula in G2 and fill down. This just takes the data in column F and eliminates the blank cells.

Formula:

=IFERROR(INDEX($F$2:$F$17,SMALL(IF($F$2:$F$17<>"",ROW($F$2:$F$17)-MIN(ROW($F$2:$F$17))+1),ROWS($1:1))),"")

...confirmed by pressing CTRL+SHIFT+ENTER to activate the array, not just ENTER. You will know the array is active when you see curly braces { } appear around your formula. If you do not CTRL+SHIFT+ENTER you will get an error or a clearly incorrect answer. Press F2 on that cell and try again.

	A	B	C	D	E	F	G
1	Date	X	Y	Z	W	SOLUTION
2	01/07/2010	TRUE	FALSE	TRUE	FALSE	01/07/2010	01/07/2010
3	23/12/2010	FALSE	FALSE	TRUE	FALSE	23/12/2010	23/12/2010
4	05/06/2011	FALSE	FALSE	TRUE	FALSE		23/11/2011
5	09/10/2011	FALSE	FALSE	TRUE	FALSE		23/12/2012
6	23/11/2011	TRUE	FALSE	FALSE	FALSE	23/11/2011	04/04/2014
7	02/03/2012	TRUE	FALSE	FALSE	FALSE
8	05/05/2012	TRUE	FALSE	FALSE	FALSE
9	06/07/2012	TRUE	FALSE	FALSE	FALSE
10	23/12/2012	FALSE	TRUE	FALSE	FALSE	23/12/2012
11	02/05/2013	FALSE	TRUE	FALSE	FALSE
12	04/06/2013	FALSE	TRUE	FALSE	FALSE
13	02/11/2013	FALSE	TRUE	FALSE	FALSE
14	05/02/2014	FALSE	TRUE	FALSE	FALSE
15	04/04/2014	FALSE	FALSE	FALSE	TRUE	04/04/2014
16	22/07/2014	FALSE	FALSE	FALSE	TRUE
17	12/05/2015	FALSE	FALSE	FALSE	TRUE