Imaginary part is the part of a complex number that is not real, in your example you have $5+3i$, there is no $3i$ on the real number axis as $(3i)^2=-9$ which doesn't work. However a complex number may also contain a real part, the number $5$.
That is you are basically talking about the coordinates in the XY-plane of complex numbers and their respective coordinates with real and imaginary part. However real numbers, when spoken of alone, is only on the "x" axis of this 2 dimensional plane, equally so you can talk about numbers only on our "Y" axis, which are numbers that only have an imaginary component but no real component.
Complex numbers in the most general sense however have both an imaginary component (The y-axis commonly) and a real component (the x-axis component)
This is why we can write complex numbers as, instead of $5+3i$ as $(5,3)$ instead.
To draw the analogy further, the imaginary/real part of a complex number can be said to be the "coordinates" of a point, while when you talk about imaginary number, it's like talking about the y-value alone and real numbers alone are just x-values.