Can a novice safely splice in wire to lengthen 5V charging cable?
For a first attempt you have achieved an excellent result.
The result should be safe and reliable. 
Cosmetically the result could be somewhat better but I have seen far far far worse in use and working long term.

The key points to consider are:


The output wires should connect to the same input wires as they did before the extension was made. Yours obviously do as the charger charges. However, this is an easy thing to get wrong and people sometimes do. The result may be as minor as "won't work" or as major as "charged device and/or charger destroyed".  

It pays to establish some way of determining which is the right and wrong way of connecting the wires. This is even more crucial when there are more than two wires.

You obviously got it right :-).
The connections should be mechanically robust and not rely on the solder for strength.   

You got it right.
The solder joints should meet guidelines for good joints.
Solder should flow and "wet" wire in both joined wires, be of correct appearance (smooth and shiny for lead 60-40 solder, less shiny for lead free solder) wires. Not too much and not too little solder.    

You did well enough.
Your competence will improve with experience.
The insulation should cover each bare conductor separately and completely. Yours does.  

You did not show the heatshrink. It should extend past the conductor at both ends and when shrunk should not be mechanically removable without destroying it.
The outer insulator should be robust enough to maintain overall insulation integrity for more than the desired lifetime of the connection.  

Yours sounds good. The outer tape MAY fray and unwind somewhat over time but the inner large heatshrink should render this unimportant. 




The most significant improvement you could aim at is improving the joining of the two wires. What you have done is entirely acceptable - but, the bare wire outside the joint proper serves no great purpose. This can occur due to insulation pullback/shrinkage when soldering. This is minimised by learning to solder faster :-). 

A way to minimise join length is to decide how many wraps each wire will make around the other 'target wire", decide how much target wire length is needed, and start winding one wire around the other at the desired length away from the target wire's insulation - ie usually quire close. When both wires have been wrapped onto their "target" wires there is no bare exposed wire between the join and insulation on either wire.



Mention was made of possible breakage at the end of the stiff solder sections and that strain relief in this area may help longevity.

This is a valid concern but unlikely to cause a short to medium term problem in normal use with normal handling. If you want to retrofit strain relief you can do so by taping or shrink tube fixing a stiff or semistiff stick/rod to the outside of the join such that it protrudes beyond the stiff soldered portion at either end. The wire leaving this portion is flexible and less liable to fatigue. Allow a small length at either end where the rod is not bonded to the wire so it exits with minimum stress.