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\[\int\limits_{b}^{a} \cos 5x= \frac{ -1 }{ 5 }\sin 5x (a \to b)\]

nope it wont go that way

In short, the 1/5 comes from the substitution for dx, which depends on the sub you make for 5x.

ahhh the substitution rule makes sense x.x stupid me. THanks!