Fran owes SmithCo. $\backslash (\backslash$$ $10,000\backslash ).$ The state where she and the company are located has a $4$ year statute of limitation on collecting the kind of debt she has. She does not have the money and does not pay, and $5$ years passes. Then, Fran inherits a reasonable amount of money, and she sends SmithCo a check for $\backslash (\backslash$$ $2,500\backslash ).$ A year later, she has not made any further payments, and SmithCo. sues.

Can SmithCo now sue for the remaining $\backslash (\backslash$$ $7500\backslash )?$