HP has been known to restrict their laptops to only work with certain very specific wireless adapters. You'll have to do some research to see if yours is one. If not, pick up two inexpensive Intel 5100 wireless cards, they should be available for pretty cheap on ebay. Intel wireless cards are very good, avoid Atheros.
I have a Dell Inspiron 9400 (also known as the E1705). Probably very similar to your smaller E1505. I upgraded its internal Mini PCIe wifi to an Intel 5100 card (A/B/G/N, 2.4 and 5GHz) without issue.
I just had to make sure to get the "full-height" version. The 5100/5300 Intel cards come in full and half height. Half-height is for newer laptops. Newer wifi cards (like Intels 6100 and 6300) are half-height only. Half would work in older laptops with a bracket or jury-rigged attachment.
As stated above, your HP might not be upgradeable. It's slot might be locked to HP-approved cards.
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