It seems these terms are used interchangeably. Are they the same thing? Do they all refer to the points in space that are given 5-letter names?
No, they are not interchangeable and indeed, have well defined meanings.
A fix is an arbitrary point in space used to establish current position calculated by referring to external references. You take a fix to determine where you are now. A fix might be permanent, for example a compulsory reporting point, or it might be determined by the pilot in advance in order to fly a non-airways route (e.g. when flying VFR) and then checked along the way using dead reckoning and reference to external systems or features to check that the plan is being flown accurately. It might also be requested by ATC, e.g. "report when overhead the railroad yard" or calculated to establish where you are, e.g. taking a fix from an astrolabe on a night oceanic crossing.
A waypoint is fixed point in 2D space (latitude and longitude) used to define points along a route. They are named, and are referenced in a plan. You fly from one waypoint to the next, along a route. A waypoint is where you are flying to. It is normally positioned where there is a change of course or altitude.
These are the navigation positions given the 5 letter names you ask about.
An intersection is where two airways cross. Here, the Victor airways 15 and 76 cross at the intersection. In this particular case, the chart symbol further shows that the V76 airway does not use the intersection, in which case the chart will include a note of the intersection usage.
Now sorry about this, but having said they are not interchangeable, it's not that simple. A waypoint is also a fix (a fix is any 2D point). But you do not call a waypoint a fix. A fix is a 2D point which is not a waypoint, but is used for navigation. A fix might be also be a lat and long defining the beginning of an arrival or departure procedure where you leave or enter an airway.
An intersection is also a fix, but it only exists to define where two airways cross (or where any other 2 lines cross, e.g. the 170 degree and 046 degree radial from two NDB beacons) so is called an intersection, not a fix.
In that sense, they are all fixes but the name has meaning.
The definition of fix above by Simon is "close" but not perfect. The definition appears to be implying that the fix just for "own ship", that is, my present position. The fix IS an arbitrary point in space. The definition should stop there. A fix MAY be used if needed to help establish your current position or may even be the estimate of your current position. You may want to get a fix on some other entity such as a coastline feature or another aircraft or vessel. For example, one generates a RADAR fix on an aircraft by knowing the location of the RADAR antenna, the azimuth angle the RADAR was pointing when "painting" the aircraft/target, and the duration of time for the RADAR signal to travel to and return from a reflecting aircraft. Thus a "fix" may have nothing to do with establishing one's current position.