To arrange the given elements in increasing order of electronegativity, we need to analyze their positions in the periodic table and understand the periodic trends of electronegativity.

Electronegativity is the tendency of an atom to attract a shared pair of electrons towards itself in a covalent bond.

Periodic Trends:
1. Across a period (left to right): Electronegativity increases because the effective nuclear charge increases and the atomic size decreases, drawing bonding electrons closer to the nucleus.
2. Down a group (top to bottom): Electronegativity decreases because the atomic radius increases and the shielding effect of inner shells increases, making it harder for the nucleus to attract bonding electrons.

Now, let's identify the positions of the given elements in the periodic table:
- Carbon (C): Period 2, Group 14
- Nitrogen (N): Period 2, Group 15
- Oxygen (O): Period 2, Group 16
- Fluorine (F): Period 2, Group 17
- Silicon (Si): Period 3, Group 14 (directly below Carbon)

Comparing Period 2 Elements (C, N, O, F):
Since these elements are in the same period, their electronegativity increases from left to right:
$C<N<O<F$

Comparing Silicon (Si) and Carbon (C):
Silicon lies directly below Carbon in Group 14. Since electronegativity decreases down a group:
$\mathrm{Si}<C$

Combining these two comparisons, we get the overall increasing order of electronegativity:
$\mathrm{Si}<C<N<O<F$
This corresponds to the order: Silicon < Carbon < Nitrogen < Oxygen < Fluorine.