The listing of globular clusters by GCL numbers comes from Alter, Ruprecht and Vanysek's Catalogue of Star Clusters and Associations. Corwin informs me that he has a copy of the second edition by Alter, Balazs and Ruprecht, which was published as 5.75 by 8.25 inch file cards filling a 16.5 by 9.25 inch box that weighs 22 pounds(!) The card for GCL 4 states that it was discovered by Dejč, at (1950) RA 02 34.6, Dec +20 56, and has a magnitude of 9.7. Per ADS, Dejč published his discovery as A(lexander) N(ikolaevich) Deutsch in the Russian Astronomicheskii Tsirkulyar Vol. 259, pp. 1-2 (1963), but whether there is anything in that publication that would change the information on the file card is unknown, since no one I know has access to such an old circular. Karimova and Kholopov confirmed the discovery on page 2 of the same circular, so there is presumably a cluster somewhere that corresponds to GCL 4, but where is definitely not the position on the file card. So whatever GCL 4 is, unless the original Tsirkulyar can be found and does not agree with the file card, GCL 4 is well and truly "lost".

Note About PGC Designation: Although HyperLEDA assigned a PGC designation to this object (even though it isn't a galaxy), a search of the database for that designation returns no result; so the designation is shown in quotes.

Physical Information:

Physical Information: LEDA misidentifies this as a spiral galaxy (type Sd); NED lists it as a cluster.

Discovery: Shakhbazian 1957, based on its "stellar" appearance in DSS images.
Physical Information: The designation "GCL 16" is now deprecated, as SDSS images show that this not a cluster of stars (as it appears to be in DSS images), but is a very compact, very distant cluster of galaxies (namely, SHK 001). Of the 17 galaxies apparently in the cluster, six have PGC designations, and all six have similar recessional velocities, indicating that many, if not all of the galaxies in the images below are members of a cluster (the last image labels the galaxies that have designations in NED. LEDA or SIMBAD). The recessional velocities for the six PGC objects have a range of 1650 km/sec, but it is not unusual for a cluster of galaxies, particularly such a compact one, to have "peculiar velocities" (random motions relative to their neighbors) in that range, and in comparison with the average recessional velocity the variation is small.
 Based on the cluster's recessional velocity relative to the Cosmic Background Radiation of 35325 km/sec (and H₀ = 70 km/sec/Mpc), a straightforward calculation indicates that SHK 001 is about 1645 million light-years away, in reasonable agreement with the only redshift-independent distance measurement for one of the cluster members of about 1615 million light-years. However, for objects at such distances we should take into account the expansion of the Universe during the time it took their light to reach us. Doing that shows that the cluster was about 1435 million light-years away at the time the light by which we see it was emitted, about 1520 million years ago (the difference between the two numbers being due to the expansion of the intervening space during the light-travel time). Given that and its apparent size of about 1.35 by 0.9 arcmin (from the images below), SHK 001 is about 565 thousand light-years across, or only about a quarter of the distance from our galaxy to the Andromeda Galaxy, so it is definitely a "compact" cluster.
Note: PGC 32808 = 32809 is listed in LEDA as only the brighter of two galaxies (which is also the brightest member of the cluster), but in the description of SHK 001 the designation refers to both the brighter northwestern galaxy and its fainter southeastern companion. To deal with this problem, I have labeled only the brighter galaxy as PGC 32808, and show it and its companion as SHK 001-1 and SHK 001-2.

Physical Information: (References: Corwin, Baumgardt, Odenkirchen and Grebel (2002), Gieles et al. (2021))
 The present distance of Palomar 5 from the Sun is roughly 21000 to 25000 parsecs (68500 to 81500 light-years), while its present galactocentric distance is about 17000 to 17500 parsecs (55500 to 57000 light-years). The motion of cluster stars relative to their surroundings suggest that the cluster orbits the galaxy about once every 250 to 3o0 million years, with a perigalaxion in the range of 15 to 17 thousand light-years and an apogalaxion of about 55 to 60 thousand light-years. The cluster itself is very small, containing only about 10 to 15 thousand Solar masses, but "tidal streams" containing stars lost by the cluster since its formation extend more than 20 degrees in front of and behind the visible cluster (these streams were discovered by Odenkirchen and Grebel in 2002 using early SDSS data). It is thought that the mass of the tidal streams is close to half again the mass still remaining in the original cluster. Corwin's apparent diameter for the central cluster is about 2.5 arcmin, which at a distance of 75000 light-years would correspond to about 55 to 60 light-years, but various references list its half-mass diameter as 130 to 180 light-years, so the actual size of the cluster is very uncertain.
 Gieles' study states that there are more than 100 stellar-mass black holes (the remnants of supernova explosions) within the cluster, with typical masses for the black holes of about 20 M_☉, and that those black holes make up about 20% of the mass of the cluster. Since the lives of stars that form such black holes are very short, all of them must have formed and died in the earliest stages of the cluster's formation, between 11.5 and 12 billion years ago. Since then, smaller stars have been more efficiently scattered by the gravitational influsence of the Milky Way, leaving the black holes concentrated in the inner portion of the original cluster; and perhaps a billion years from now, most of its remaining "normal" stars may have been lost to the tidal streams, and the cluster itself may consist of nothing but its black holes, making the cluster an invisible part of an even more extended "stream".