Time-invariant system question
You were given

$$ x_2(t) = x_1(t-T)$$

If you apply the transformation \$t\to t-T\$ to the expression \$2t-5\$, you get \$(2t-5)-T=2t-5-T\$, not \$2t-5-2T\$.

Your expression for \$y(t)\$ involves multiplying the argument of \$x(t)\$ by 2, but that's irrelevant to the question of determining \$x_2(\cdot)\$ from \$x_1(\cdot)\$.