Being that you don't own the access point, you will have to work with your end only to improve your ability to receive and get to that access point.

The access point if a more commercial outdoor unit will probably put out a good amount of power (at least 100mW or more). This means if you improve your power to it, it certainly can help.

Antenna will be the biggest factor in getting this range. Next is power.

I suggest you get a high power USB device such as EnGenius Eub-362 EXT. It puts out 200mW and has an RP-SMA connector to allow you to change out the antenna. You probably should consider a high gain directional antenna with a pigtail cable. This still might not be enough... so look next.

Another option is to go with an outdoor client bridge such as an EnGenius EOC-2610. This unit puts out 600mW and comes with a built in 10dbi antenna. It also has an RP-SMA connector to choose an external antenna instead. I'd personally opt for one of those 24dbi grid antennas you can get for around $50 and an RP-SMA to Type N pigtail. This unit is power over ethernet so all you'd have running to it is your cat 5. At $99 I'd get the 2610 first, then if the 10dbi antenna still isn't enough, then go buy the 24dbi grid. You may not need even need it. Also, higher above ground is always better.

RFMAN!