To find the original length of the string, we use the relationship between tension, elasticity constant ($ K $), and the change in length of the string.

Given the equation for tension:

$ \mathrm{T} = \mathrm{K}(\ell - \ell_0) $

where $\ell$ is the length of the string under tension and $\ell_0$ is the original length.

When the tension is 5 N, the equation becomes:

$ 5 = \mathrm{K}(1.4 - \ell_0) $

When the tension increases to 7 N, the equation is:

$ 7 = \mathrm{K}(1.56 - \ell_0) $

By setting up a ratio from the two equations, we have:

$ \frac{5}{1.4 - \ell_0} = \frac{7}{1.56 - \ell_0} $

Solving this proportion gives us the original length $ \ell_0 $:

$ \ell_0 = 1 \, \mathrm{m} $

Thus, the original length of the string is 1 meter.