Let's call the number of nickels the woman has "n". Then the number of dimes she has is "n + 5".
The total value of the nickels is 0.05n, and the total value of the dimes is 0.10(n + 5).
We know the total value of the coins is $1.70, so we can set up the following equation:
0.05n + 0.10(n + 5) = 1.70
Expanding the expression for the dimes:
0.05n + 0.10n + 0.50 = 1.70
Combining like terms:
0.15n + 0.50 = 1.70
Subtracting 0.50 from both sides:
0.15n = 1.20
Dividing both sides by 0.15:
n = 8
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So the woman has 8 nickels.