Alright, let's work through 5177 times 7658 step by step
5177 × 7658 = 7658 × (5177)
+ 7658 × 7 that is equal 53606
+ 7658 × 70 resulting in 536060
+ 7658 × 100 that results in 765800
+ 7658 × 5000 that equals 38290000

= 39645466
