Let x be the first odd integer, then the next two odd consecutive integers are x+2 and x+4.

Equation: x + (x+4) = 5(x+2) - 87

Solution: x = 25, third integer = 29.

Step-by-step explanation:

Let x be the first odd integer, then the next two odd consecutive integers are x+2 and x+4.

According to the problem statement:

The first and third of three odd consecutive integers are added: x + (x+4) = 2x + 4

The result is 87 less than five times the second integer: 5(x+2) - 87 = 5x - 73

Now we can set up an equation by equating the expressions we just found:

2x + 4 = 5x - 73

Solving for x:

2x + 4 = 5x - 73

2x + 77 = 5x

77 = 3x

x = 25.67

Since x must be an odd integer, we can conclude that x = 25. Thus the three odd consecutive integers are 25, 27, and 29, and the third integer is 29.