CPU mostly. An i5 isn't going to be able to swing streaming 1080p@60. OBS mostly just uses the GPU for source scaling and compositing.
Local recording, you can just throw gobs of bitrate at it on x264 Ultrafast to compensate for the CPU, and 20-30mbps to compensate for the poor quality compression of Ultrafast.
Real-time video encoding is an EXTREMELY heavy task though. Even something like an i7-5820k is going to struggle a good bit with 1080@60@Veryfast. Even at that point, it's going to want around 5-6000kbps as a starting streaming bitrate.
So no, your current rig can't stream 1080@60. But you can downscale and use a lower fps rate to bring it to within what your hardware can handle. 720p@30fps is the recommended point for non-partnered streamers, as it fits into the 2000kbps max recommended non-partner bitrate quite conveniently.