And I'm not sure if they're needed, but the relativistic eq's are:

KE = mc^2/sqrt(1-(v/c)^2)
p = mv/sqrt(1-(v/c)^2)

I'm not sure if this one applies to relativistic speeds:

E = hc/λ

3. The attempt at a solution

Attempt 1:

E = hc/λ

4.8E-13 = (6.63E-34)(3E8)/λ
λ = (6.63E-34)(3E8)/(4.8E-13) λ = 4.14E-13 m

BUT answer key says 3.58E-13

If you could help, that would be great.
Sorry if it's too long, and I'm a little unfamiliar with relativistic eqn's so forgive me if I screwed up on them.

The equation you used, [itex]E = hc/\lambda[/itex], only applies to photons (or massless particles in general). So you're not going to need that one here. If you're familiar with the equation
[tex]E^2 = p^2c^2 + m^2c^4[/tex]
I'd use that. If not, you can get the velocity from
[tex]E = \frac{mc^2}{\sqrt{1 - v^2/c^2}}[/tex]
(note that that's total energy, not kinetic energy) and compute the momentum from that.