Answer
infinitely many solutions
Work Step by Step
Substituting $x=\dfrac{2}{5}y+2$ into the first equation results to
\begin{array}{l}\require{cancel}
5x-2y=10
\\\\
5\left( \dfrac{2}{5}y+2 \right)-2y=10
\\\\
2y+10-2y=10
\\\\
2y-2y=10-10
\\\\
0=0
\text{ (TRUE)}
.\end{array}
Since the solution above ended with a TRUE statement, then there are $\text{
infinitely many solutions
}$ to the given system of equations.