Type 5 is a Mind type, Type 4 is Heart type. Mind types predominately deal with Fear, while Heart types predominately deal with Sadness and Shame.
Type 5 primarily deals with the fear of being invaded, intruded upon. Type 5 is typically the most withdrawn type in the Enneagram (especially when they are Sp/Sx, not as much when they are Social first). They withdraw as a way to cope with their fear of not being able to deal with the outside world. They accumulate knowledge because they believe that will help them with encountering and handling the outside world. However, this coping behaviour commonly isolates them, because there is seemingly no end to the preparation they have to do before they feel “ready” to face the world.
Type 4 primarily deals with their sadness over being unloveable for what they deem to be an intrinsic flaw of character (that they usually cannot put a finger on – because it is not actually “real”, but due to childhood experiences they believe so). This perceived flaw makes them feel ashamed for themselves (Social 4s feel the most of that shame, Self-preservation 4s the least). Type 4s see their flaw as being shameful, but also the thing that makes them unique. As a coping mechanism, average 4s will exaggerate their unique traits, as a way to cover up their flaw(s) and be seen as a person worthy of love. Or in other words, average Type 4s equate being unique with being lovable.
Another way to look at 5 vs 4, is by recognizing the fact that Heart types are also Image types. All Types 4 are concerned with their image: their outward appearance and how other people receive it. In a way, they believe that one’s image can determine whether one is being loved or not. Type 5s don’t think that way at all, they usually care little about their image, often times they (deliberately or not) cloth themselves poorly, because they care so little. They also don’t see how their image makes people either love or hate them. Type 5 focuses mainly on their intellectual capacities, that is where their pride but also fears lie. As the Type 4 believes their image (usually of being a unique individual) brings them love and admiration, the Type 5 believes it is their intellectual know-how and brain power that will bring them the respect of others and a sense of security.
When it comes to their emotional/psychological state, Type 4s typically suffer from mood swings and/or a melancholic attitude at average to unhealthy levels, while Type 5s are typically in a state of detachment or ambivalence from many to most outside events, being a mere observer of life at average to unhealthy levels.
Generally speaking, which of the two main issues, fears and compensatory mechanisms is more dominant in you is likely the type you are. To put it in perspective, the wing type is an add-on to your personality, but the main type’s issues are always more complex and difficult for oneself. Ironically, many people are more aware and accepting of their wing type’s issues at first, because the main type’s issues are so deeply ingrained in one’s sense of self that they can be somewhat unconscious and ultimately more hurtful to oneself.
As a side note, your MBTI type gives you a hint at which of the two types you are, most likely. If you are INTP or INTJ, you are probably 5w4. If you are INFP, INFJ of ISFP, you are probably 4w5. More about MBTI-Enneagram correlations here. Click on the respective type for examples of 5w4 vs 4w5 individuals.