jmc

No $1\times 1$ squares or $2\times 2$ squares contain five black squares. Every square which is $4\times 4$ or larger does. However, a $3\times 3$ square will only contain 5 black squares if its upper left corner is black. We can choose the upper left corner of a $3\times 3$ square in $6\cdot 6=36$ ways, but for only half of these squares will the upper left corner be black. Therefore, there are $36/2=18$ $3\times 3$ squares containing at least 5 black squares. We can choose the position of the upper left square of a $4\times 4$ square in $5\cdot 5=25$ ways, so there are 25 $4\times 4$ squares. Similarly, there are 16 $5\times 5$ squares, 9 $6\times 6$ squares, 4 $7\times 7$ squares and 1 $8\times 8$ square. There are a total of $18+25+16+9+4+1=\boxed{73}$ squares containing at least 5 black squares.