You are conflating multiple concepts. A "perfect fifth" is an interval, whereas a "IV chord" is a triad built on a scale degree. The interval is a more primitive "unit" of harmonic analysis than the scale-degree-triad.
When you say that the IV and V chords "are" perfect fifths, it appears that what you mean is that the root of each chord is a perfect fifth away from the tonic of the scale.
This is absolutely a reasonable thing to take note of! But on its own, it doesn't really mean much. Here are some questions you ought to ask yourself:
- Why does the interval between the root of a chord and the tonic matter?
- Why does the interval between any scale degree (whether used as the root of a chord or not) and the tonic matter?
- What gives different scale-degree-triads different "functions" in harmonic theory? (Or, with less music-theoretical terminology: why do we differentiate between I, ii, iii, IV, ... chords?)
The important thing to take note of here is that the concept of "intervals" is insufficient to answer any of these questions, because they involve harmonic context, which is not included in our idea of an "interval".
So, let's start by eliminating the concept of chords from your question, and ask:
Is the 4th scale-degree really a "perfect fifth" in disguise?
When phrased that way, it's not clear what's "in disguise" here, because the obvious answer is yes, the 4th is a perfect fifth away from tonic. The next step is to ask about the connection with the 5th scale degree (which we'll need to consider if we want to eventually understand the relationship to the V chord):
Is the 4th scale-degree really "equivalent to" the 5th scale degree?
Well, here we need some notion of "equivalence". Yes, each scale degree is a perfect fifth away from the tonic. But the 4th degree is a fifth down, whereas the 5th degree is a fifth up.
In other words, in order to understand scale-degrees, we need to recognize that although our idea of "interval" doesn't include a direction, we need an idea of interval with direction. This is similar to how numbers don't have "direction" in mathematics, but it's sometimes necessary to discuss a "number with direction", which we call a "vector".
Let us take a step back and consider what harmony is. A musical harmony is not just a collection of pitches; it is a collection of pitches that change over time. Thus, the "direction" in our "interval with direction" is the direction in which a pitch moves over time. A "fifth up" is found when a voice starts on a particular pitch, and then moves to a pitch a 5th above that.
So, the relationships between scale degrees have something to do with when the scale degrees are played in relation to each other. If we imagine a voice moving from the 5th degree to the tonic, that is a "fifth down"; and if we imagine a voice moving from the tonic to the 4th degree, that is also a "fifth down".
Since we can take this idea of moving between scale degrees and apply it by chordal movements by simply discussing triads built on the scale degrees instead of scale degrees on their own, we have enough context to create a less misleading version of your original question;
Is the (function of the) harmonic movement V -> I equivalent to the harmonic movement I -> IV?
The answer is, essentially, yes, depending on context! The movement I -> IV could be considered an opportunity to recontextualize IV as the new "tonic", with I as the new "dominant" (V). Though note that in most contexts, I is preserved as the tonic. This is part of why the sequence I -> IV -> V -> I works well; I -> IV "sounds good" in the same way that V -> I does, but it introduces an ambiguity, since IV may now be treated as the "new" I. The IV -> V demonstrates that IV is not functioning as the tonic, since V includes the seventh scale degree, which would be a half-step lower if the 4th scale degree were the tonic. (Concretely: in C major, C M -> F M implies that we might be moving to F major, but F M -> G M shows that we can't be in F major because we have B natural.)