If x is the smaller one, and is odd, the next consecutive odd integer is x+2.
[tex]x(x+2) = 23 + 5(x+ (x+2))[/tex]
[tex]x^2 + 2x = 23 +5(2x+2)[/tex]
[tex]x^2 + 2x = 23 + 10x + 10[/tex]
[tex]x^2 -8x - 33 = 0[/tex]
[tex](x-11)(x+3) = 0[/tex]
[tex]x = 11\textrm{ or }x=-3[/tex]
Check:
11(13) = 143
23 + 5(11 + 13) = 23 + 120 = 143, check
-3(-1) = 3
23 + 5(-3 + -1) = 3, check
Answer: 11,13 or -3,-1
