解:$(1) (-a)^8 \div (-a)^5 = (-a)^{8 - 5} = (-a)^3 = -a^3$
$(2) x^{10} \div (x^2)^3 = x^{10} \div x^6 = x^{10 - 6} = x^4$
$(3) (m - 1)^5 \div (m - 1)^2 = (m - 1)^{5 - 2} = (m - 1)^3$
$(4) (a^m)^n ·(-a^{3\ \mathrm {m}})^{2n} \div (a^{mn})^5 = a^{mn}\ \mathrm {·}a^{6\ \mathrm {m}n} \div a^{5\ \mathrm {m}n}= a^{2\ \mathrm {m}n}$