First, let's find the values of a and b using the given equations:

From A + B = 5:
A = 5 - B

From AB = -3:
(5 - B)B = -3
5B - B^2 = -3
Rearranging,
B^2 - 5B - 3 = 0
Using quadratic formula:
B = (5 ± √(5^2 - 4*-3))/2
B = (5 ± √(25 + 12))/2
B = (5 ± √37)/2

Therefore, B = (5 + √37)/2 or B = (5 - √37)/2

Similarly, A = (5 - √37)/2 or A = (5 + √37)/2

Now, calculating the product:

(a^4 + b^4) = [(a^2)^2 + (b^2)^2 - 2a^2b^2]
= [a^2 + b^2)^2 - 2ab
[(a^3 + b^3)^2 + 2a^3b^3]
[(a^2 + b^2)^2 + 2ab]
((a + b)^2 + 2ab)
(5^2 + 2(-3))
(25 + (-6))
19

The value of (a^4 + b^4) × (a^3 + b^3) × (a^2 + b^2) is 19.