Pairs with Sum divisible by 5
Python 2, 32 bytes



lambda m,n:(m*n+abs(m%5-~n%5))/5


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Adapts an idea from Arnauld. We estimate that \$1/5\$ of the \$mn\$ pairs will satisfy the mod-5 condition. Th actual value may be one higher depending on the mod-5 values of \$m\$ and \$n\$, and we bump up \$mn\$ a bit so that these make it pass the next multiple of 5.



34 bytes



lambda m,n:m*n/5+(0&lt;-m%5*(-n%5)&lt;5)


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34 bytes



lambda m,n:m*n/5+(m*n%5+m%5+n%5)/9


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36 bytes



lambda m,n:m*n/5+((5-m%5)*(5-n%5)&lt;5)


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36 bytes



lambda m,n:m*n/5+(abs(m%5+n%5*1j)&gt;4)


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36 bytes



lambda m,n:m*n/5+(m%5*5/4+n%5*5/4&gt;5)


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36 bytes



lambda m,n:m*n/5+(m%5+n%5+m*n%5/4&gt;5)


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