В чём отличие между Integer a = new Integer(5) и Integer a = Integer.valueOf(5)?

valueOf вернет значение из кэша, если аргумент лежит в кэшированном диапазоне. new всегда создаст новый объект. Все написано в самом классе Integer:

/**
 * Returns an {@code Integer} instance representing the specified
 * {@code int} value.  If a new {@code Integer} instance is not
 * required, this method should generally be used in preference to
 * the constructor {@link #Integer(int)}, as this method is likely
 * to yield significantly better space and time performance by
 * caching frequently requested values.
 *
 * This method will always cache values in the range -128 to 127,
 * inclusive, and may cache other values outside of this range.
 *
 * @param  i an {@code int} value.
 * @return an {@code Integer} instance representing {@code i}.
 * @since  1.5
 */
public static Integer valueOf(int i) {
    if (i >= IntegerCache.low && i <= IntegerCache.high)
        return IntegerCache.cache[i + (-IntegerCache.low)];
    return new Integer(i);
}

/**
 * The value of the {@code Integer}.
 *
 * @serial
 */
private final int value;

/**
 * Constructs a newly allocated {@code Integer} object that
 * represents the specified {@code int} value.
 *
 * @param   value   the value to be represented by the
 *                  {@code Integer} object.
 */
public Integer(int value) {
    this.value = value;
}