A 130mm (5 inch) scope typically has a limiting magnitude of about 13.3, so when you look at a galaxy which is designated with a magnitude of say 10.0 you would think it well within your range. Unfortunately galaxies and nebulae, unlike stars, are not points of light. What is being measured is the total light from that galaxy as if it were a point of light, so the chances are that you might not be able to see that particular galaxy. Indeed, a more realistic limit for most scopes in light polluted skies is at least 4 magnitudes less than the theoretical maximum. Galaxies and Nebulae are not called faint fuzzies for nothing.
One of the first things that the newcomer will hear about is the Messier catalogue. This is a list of faint fuzzy objects which the comet hunter Charles Messier drew up in the late 18th century in order to avoid wasting time looking at them. Nowadays this list and others like the Caldwell catalogue compiled by Patrick Moore, form the basis of many astronomers viewing. They consist of star clusters, nebulae, galaxies and the occasional star. A few are just visible to the naked eye as faint patches of light, but if viewing conditions are poor and you have a small scope of 6 in (150mm) or less it is no good looking for anything other than the very brightest clusters, galaxies and nebulae.
Star clusters, particularly the Open Clusters, are some of the most spectacular objects visible in the sky. There are two main types.
Open Clusters: These are groups of stars, usually of the same age, young and bright and without any regular shape. The most famous of these is the Pleiades, or Seven Sisters and they can be seen as a fuzzy patch even in moderately light-polluted skies. In dark skies with very keen eyesight you may be able to count all 7! It is a good object to see in a small telescope with low magnification though the group is so large that you won't see all of them at one go. Indeed this is one object best seen through binoculars.
Globular Clusters: These contain some of the oldest stars known and can contain up to one million stars. They are symetrical systems and more widely distributed than the Open Clusters, surrounding our galaxy in what is termed 'the Galactic Halo'. Of the hundred or so known clusters only 3 are visible to the naked eye, given good viewing conditions. They are most common in the southern hemisphere of the sky and, during the northern hemisphere winter when Orion is high in the sky, there are almost none visible at all. They are nowhere near as spectacular as open clusters, the best in the northern hemisphere being M13, the Great Cluster in Hercules. This is the one shown at the bottom of the home page.
Gaseous or Galactic nebulae are stellar birthplaces where fresh stars slowly condense out of the nebular material. They shine because of the stars in or around them - an Emission nebula if the stars are hot - or as a Reflection nebula if the stars are cooler.
Planetary Nebulae are neither planets nor nebulae. They are called that because in a telescope they resemble the disks of planets. They are really shells of gas surrounding hot stars evolving to the white dwarf stage. The most famous one is M1, the Crab Nebula which is in the Constellation of Taurus, not Cancer, the remnant of the supernova of 1054 - another is M57, the Ring Nebula.
One of the best known objects in the sky is the Orion Nebula, situated just below the belt of Orion. Even in moderately light-polluted skies this can usually be seen with the naked eye as a faint blob. In a small telescope you can see both the four stars of the Trapezium and the associated nebula fuzziness. However, you won't see any colour even in the larger telescopes. For that you need a reasonably long-exposure photograph though because of the intensity of the inner core it is difficult to get good single images of the whole. What you can see in colour will be some of the stars in the Orion constellation, in particular the red Betelgeuse at the top left of the constellation. Bodes Nebula (M82) and the nearby cigar-shaped M81 in Ursa Major should also be visible through a small scope, and even binoculars if you know where to look and light pollution isn't too bad.
Galaxies: During the summer months our own Milky Way Galaxy can be seen with the naked eye if the light pollution isn't too bad. A band of light stretching across the sky - so magnificent in a really dark sky that newcomers often think it is cloudy! And the other Galaxy which everyone has heard about is M31, the Andromeda Galaxy. Other galaxies visible with small scopes include M51 (the Whirlpool Galaxy), M27 (the Dumbbell Nebula) and M57 (the Ring Nebula). Others that you will see mentioned include M8 (the Lagoon Nebula), though this is often too low in the sky to be easily seen. But most galaxies will never be more than faint smudges in small scopes.
Again, use the computer programs and magazines to find out exactly what you can see, but bear in mind that the magazines are always, in my opinion, too optimistic and do not take enough account of light pollution. Having said that may I recommend Robin Scagell's 'Stargazing with a Telescope'. Not only is it a very good and informative read, but it has some very useful lists of interesting objects to observe. These are arranged in order of declination, which means that the objects at the top of the lists are the highest in the sky for northern hemisphere observers - vice versa for the southern hemisphere.
Finally, remember, practice makes perfect. Experienced observors always see more than beginners.