If the binary operation `**` on the set Z of integers is defined by `a**b=a+b-5`, then write the identity element for the operation `'**'` in Z.

Answer

To find the identity element for the binary operation defined by \( a ** b = a + b - 5 \) on the set of integers \( \mathbb{Z} \), we need to determine an element \( e \) such that for any integer \( a \):

\[ a ** e = a \]

### Step 1: Set up the equation
Using the definition of the operation, we can express the identity condition:

\[ a ** e = a + e - 5 \]

### Step 2: Set the equation equal to \( a \)
Since we want \( a ** e \) to equal \( a \), we set up the equation:

\[ a + e - 5 = a \]

### Step 3: Simplify the equation
To isolate \( e \), we can subtract \( a \) from both sides of the equation:

\[ e - 5 = 0 \]

### Step 4: Solve for \( e \)
Now, we can solve for \( e \) by adding 5 to both sides:

\[ e = 5 \]

### Conclusion
Thus, the identity element for the operation \( ** \) in \( \mathbb{Z} \) is:

\[ \boxed{5} \]

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