One can use Cat5e, but it has to be full cable with all the pins connected. Giga needs to use all the conductors in standard cat5e or CAT6 cable.
That said Giga is rather Finicky when used in Home networks.
Many users get around 35 to 45 MB/sec. LAN transfer (B=Byte). While not being full Giga it is still x5 faster than 100Mb/sec LAN that usually yield 8 to 10 MB/sec. transfer on end users humble networks.
Good optimized Giga system can yield up to this.