Hi Chris,
The below code will delete feature classes from the 'test.gdb' that contain '1405' or '1305'. It will also rename any feature class that contains '1406' to text before the underscore. For example, 'SouthernWells_1406' would be renamed to 'SouthernWells'.
import arcpy
from arcpy import env
env.workspace = r"C:\temp\python\test.gdb"
for fc in arcpy.ListFeatureClasses("*"):
if '1405' in fc or '1305' in fc:
arcpy.Delete_management(fc)
elif '1406' in fc:
arcpy.Rename_management(fc, fc.split("_")[0])