I am a new ham and wish to mount a center-fed G5RV dipole antenna under the eaves of my house, where I have a 78' clear run available two stories above ground. The problem is a metal rain gutter which runs parallel to the antenna, about 3 feet to the side of it. My concern is that the gutter would essentially represent a short-circuit to the dipole as it is just a fraction of a wavelength away, making the antenna ineffective as a radiator. Is this true?
The gutter will be in the near field of the dipole. It may affect the tuning of the dipole or its radiation pattern, but it will not "short out" the dipole as long as the dipole wires are not in direct contact with the gutter or downspouts.
You may have other conducting materials in the near field such as siding, sofette trim and conduit. Any of these may also affect the antenna.
An antenna very close to a house may pick up more electrical interference that is being created within the house from things like switching power supplies, television sets and LED lamps. The opposite can also be true when transmitting. The close proximity of the antenna to the house may cause interference with speakers, telephones, smoke alarms, arc fault breakers, etc.
Your G5RV design uses window line as part of its feedline. Make sure to keep this at least six inches from any metal surfaces such as siding. If you have an antenna tuner and don't require a long feedline, you will be better off feeding the dipole directly with coax connected to a choking balun. This will reduce noise pickup and allow the coax to be freely run where it is convenient.
This may all sound like doom and gloom but take heart because many hams successfully use antennas in similar situations and have great success. The best advice is to give it a try to see how it works for you. Start with 10 watts or so of transmit power and see how it behaves before increasing your power. You may need to take some remedial actions but most importantly, you will be on the air!
I agree with Glen, but if you wanted to be more sure that the gutter is not affecting the antenna very much you could try cutting a short section (even 1 inch or less) of it every so often (say 10 feet or less) and filling it with plastic gutter (use silicone to seal it, of course). That would make the gutter too short in each section to be a serious problem.