The ordered pair `(5,2) ` belongs to the relation
`R={(x,y):y=x-5,x,y in Z}`

Explanation

To determine whether the ordered pair (5, 2) belongs to the relation \( R = \{(x, y) : y = x - 5, x, y \in \mathbb{Z}\} \), we will follow these steps:

### Step 1: Understand the Relation
The relation \( R \) is defined such that for any ordered pair \( (x, y) \), the value of \( y \) must be equal to \( x - 5 \). This means that for any integer \( x \), we can find a corresponding integer \( y \) by subtracting 5 from \( x \).

### Step 2: Substitute the Values
We need to check if the ordered pair \( (5, 2) \) satisfies the relation. Here, \( x = 5 \) and \( y = 2 \).

### Step 3: Calculate \( y \) using the Relation
Using the relation \( y = x - 5 \):
\[ y = 5 - 5 = 0 \]

### Step 4: Compare the Calculated \( y \) with Given \( y \)
Now we compare the calculated value of \( y \) with the given value of \( y \) from the ordered pair:
- Calculated \( y = 0 \)
- Given \( y = 2 \)

### Step 5: Conclusion
Since \( 0 \neq 2 \), the ordered pair \( (5, 2) \) does not satisfy the relation \( R \). Therefore, the ordered pair \( (5, 2) \) does not belong to the relation \( R \).

### Final Answer
The ordered pair \( (5, 2) \) does not belong to the relation \( R \).

---