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The gigabit Ethernet standard is designed to support Category 5 cable. Here are the details from the 802.3 Ethernet standards document, section 40.7.1 - Cabling system characteristics:
"1000BASE-T requires 4-pair Class D cabling with a nominal impedance of 100 ohms, as specified in ISO/IEC 11801:1995. The cabling system components (cables, cords, and connectors) used to provide the link segment shall consist of Category 5 components as specified in ANSI/TIA/EIA-568-A:1995 and ISO/IEC 11801:1995."
Category 5 and category 5e cables are physically identical. The only difference were the verification tests used to qualify a cable as category 5e.