Answer
$v = 0.9999999896~c$
Work Step by Step
We can find $\gamma$:
$E = \gamma~mc^2 = 6.5~TeV$
$\gamma~mc^2 = (6.5~TeV)(\frac{1.6\times 10^{-19}~J}{1~eV})$
$\gamma~mc^2 = (6.5\times 10^{12}~eV)(\frac{1.6\times 10^{-19}~J}{1~eV})$
$\gamma~mc^2 = 1.04\times 10^{-6}~J$
$\gamma = \frac{1.04\times 10^{-6}~J}{mc^2}$
$\gamma = \frac{1.04\times 10^{-6}~J}{(1.67\times 10^{-27}~kg)(3.0\times 10^8~m/s)^2}$
$\gamma = 6919$
We can find the speed when $\gamma = 6919$:
$\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$
$\sqrt{1-\frac{v^2}{c^2}} = \frac{1}{\gamma}$
$1-\frac{v^2}{c^2} = \frac{1}{\gamma^2}$
$\frac{v^2}{c^2} = 1-\frac{1}{\gamma^2}$
$v^2 = (1-\frac{1}{\gamma^2})~c^2$
$v = \sqrt{1-\frac{1}{\gamma^2}}~c$
$v = \sqrt{1-\frac{1}{(6919)^2}}~c$
$v = \sqrt{0.999999979}~c$
$v = 0.9999999896~c$
