What are some consequences of putting quotes in a WHERE clause for an integer column?
Both do the same and you won't be able to measure any difference in performance.

Details

This is a string literal or string constant: '5'

The manual:


  A string constant in SQL is an arbitrary sequence of characters
  bounded by single quotes ('), for example 'This is a string'. To
  include a single-quote character within a string constant, write two
  adjacent single quotes, e.g., 'Dianne''s horse'. Note that this is not
  the same as a double-quote character (").


If there is no context from which a type can be derived, a string literal is initially assumed to be type text. (Not the case in your example.)

The manual once more:


  The explicit type cast can be omitted if there is no ambiguity as to
  the type the constant must be (for example, when it is assigned
  directly to a table column), in which case it is automatically coerced.


This is a numeric literal or numeric constant: 5

The manual:


  A numeric constant that contains neither a decimal point nor an
  exponent is initially presumed to be type integer if its value fits in
  type integer (32 bits); otherwise it is presumed to be type bigint if
  its value fits in type bigint (64 bits); otherwise it is taken to be
  type numeric. Constants that contain decimal points and/or exponents
  are always initially presumed to be type numeric.


So a numeric literal starts out with a specific type. It may then be cast to a different type as the context requires - if such a cast is defined. That's a subtle, but important difference - which makes no effective difference in your case, since 5 is initially integer, which is exactly the type it needs to be.

But it matters in other cases. Try this:

CREATE TEMP TABLE tbl1 (t int);
SELECT * FROM tbl1 where t = '0';         -- works!
SELECT * FROM tbl1 where t = int '0';     -- works!
SELECT * FROM tbl1 where t = int2 '0';    -- works!
SELECT * FROM tbl1 where t = 0;           -- works!

CREATE TEMP TABLE tbl2 (t text);
SELECT * FROM tbl2 where t = '0';         -- works
SELECT * FROM tbl2 where t = text '0';    -- works
SELECT * FROM tbl2 where t = varchar '0'; -- works
SELECT * FROM tbl2 where t = 0;           -- fails !!!



ERROR:  operator does not exist: text = integer



Because the numeric literal starts out as integer and there is no assignment cast defined for integer --> text. (Any type can be cast to text with an explicit cast (0::text) but that cast is not assumed here.)