The number of integers, greater than 7000 that can be formed, using...

Case $1$

forming $4$ digit number,

When $7$ is at $1000 ' \text{s}$ place

7___,

So total number of ways will be $4 \times 3 \times 2 = 24$ ways,

Case $2$

forming $4$ digit number when $8$ is at $1000 ' \text{s}$ place

8___,

So total number of ways will be $4 \times 3 \times 2 = 24$ ways,

Case $3$

forming $5$ digit number,

So total number of ways will be $5 ! = 120$ ways,

Now adding all the cases we get, $120 + 24 + 24 = 168$ ways.