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(D) Let the $5$-digit number be $d_1 d_2 d_3 d_4 d_5$. Since the number $> 50000$,$d_1 \in \{5, 6, 7\}$.We are given $d_1 + d_5 \le 8$.Case $1$: $d_1

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$4607$

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(D) Let the $5$-digit number be $d_1 d_2 d_3 d_4 d_5$. Since the number $> 50000$,$d_1 \in \{5, 6, 7\}$.We are given $d_1 + d_5 \le 8$.Case $1$: $d_1 = 5$. Then $5 + d_5 \le 8 \implies d_5 \in \{0, 1, 2, 3\}$. There are $4$ choices for $d_5$.For $d_2, d_3, d_4$,each can be any of the $8$ digits $(0-7)$. So,$8 	imes 8 	imes 8 = 512$ ways per $d_5$. Total $= 4 	imes 512 = 2048$.Case $2$: $d_1 = 6$. Then $6 + d_5 \le 8 \implies d_5 \in \{0, 1, 2\}$. There are $3$ choices for $d_5$.Total $= 3 	imes 512 = 1536$.Case $3$: $d_1 = 7$. Then $7 + d_5 \le 8 \implies d_5 \in \{0, 1\}$. There are $2$ choices for $d_5$.Total $= 2 	imes 512 = 1024$.Summing these: $2048 + 1536 + 1024 = 4608$.Since the number must be greater than $50000$,we exclude the case $50000$ (where $d_1=5, d_2=0, d_3=0, d_4=0, d_5=0$).Thus,the total count is $4608 - 1 = 4607$.

The number of different $5$-digit numbers greater than $50000$ that can be formed using the digits $0, 1, 2, 3, 4, 5, 6, 7$,such that the sum of their first and last digits is not more than $8$,is:

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