USB 3.0 to esata

According to the specs, your laptop does have a cardbus slot, although it is referred to as an ExpressCard/54 (/34 compatible). Something like this should be suitable: LaCie - LaCie USB 3.0 ExpressCard/34

Your laptop doesn't say anything about USB 3.0, so you would have known right away that you'd be limited to USB 2.0 speeds. However, I used several eSATA drives as well, and they do offer much better speeds than when connected by USB 2.0.

most laptops have tons of unused components that just need a bit of soldering and a couple connectors to come to life (and someone that knows where to solder and what, much harder to find), so don't feel bad over not using e-sata ports.

Your laptop has a "One ExpressCard/54 slot (also supports ExpressCard/34)". Which is awesome. There are tons of USB 3.0 adapters for expresscard slots.
Of course they won't deliver full USB 3.0 speeds due to technical limitations, but it's usually close enough to leave USB 2.0 in the dust.

This Is a branded slim-factor 2xUSB 3.0 card for expresscard 54 slot. With a connector for additional power that you may need to connect to a USB 2 if the USB 3 device is really hungry. Much better than what Dwarf found.

If you really want to throw the less money possible at it, this is the same, but not branded. I had one in my hands and it worked fine after I installed drivers.
The guy that bought it came to me because the driver disk shipped with it is worthless (their drivers don't work), and you have to go and download the drivers yourself, from this site (the chip's manufacturer).

Seems legit. But it's the toss of a coin with these things, you know.
It does not indicate the chip name, the other I linked and the one I had in hand had "BC618T" (chip name) printed after the "5Gbps", but the rest seems the same. Unless it is a knockoff of a knockoff, it's likely another production run of the same.

The Usual Warning: the fact that I had one and worked does not make me responsible if the one you buy is trash (in fact, people said even Star Tech one was trash so you may still be happy). I'd buy a couple just to be sure, if both work you can sell the second one to friends with a profit.

The power connector (the usb cable with the plug you see in the pic) allows you to add the power from another USB 2.0 port (500 mA) on top of the power provided by the expresscard 54 slot (unknown but likely not more than 1 A) by placing said cable in a USB 2.0 of your laptop, and the other end of the cable in the connector for it that is between the two USB 3.0 ports in the expresscard.

Since a USB 3.0 port is supposed to provide up to 900 mA, such additional power cable is usually unnecessary if you have only one USB 3 device plugged, but may be required to operate two USB 3.0 devices, thus using the card to its full potential. (just remember that it's still an expresscard, so if you transfer stuff from both devices at the same time, the speed will drop to the floor)

If you look at cards with f-ugly form factor (click on technical specification tab in that page), they say "Due to the power limitations of the ExpressCard interface this adapter cannot supply 900mA of current to both ports. Some devices like External 2.5” Hard Drives may require an additional power adapter. "
So they aren't just f-ugly and can be beheaded with frightening ease, but they can use only one of the two ports at the full potential.

looks like we edited posts at the same time, I think my post above yours contains the answer for that now.

Also note that my "support" for that card is limited. I can help finding drivers if for some reason it's not working with the linked ones above but not much more.

USB3 has nice specs but eSata is faster. At least that is my experience on a system that has both USB3 and eSata using the same HDD in corresponding external enclosures. There seems to be a lot of overhead with USB3.