Scrape a jobs board and keep persistent record
Code Quality and Other Improvements


I would use a cursor and a connection as context managers to avoid having to explicitly close them and let Python safely close them if an error happens:

with sqlite3.connect('jobs.db') as connection:
    with connection.cursor() as cursor:

making the query defined as a multi-line string could benefit readability:

cursor.executemany("""
    INSERT INTO 
        jobs 
    VALUES (?, ?, ?, ?, ?)""", new_result)

watch for PEP8 code style violations - for instance, organize imports in a proper way


Performance

We can definitely do better performance-wise:


switch from lxml to html.parser (requires lxml to be installed):

BeautifulSoup(page, "lxml")

since you need only span elements, let BeautifulSoup parse only them:

from bs4 import BeautifulSoup, SoupStrainer

parse_only = SoupStrainer('span')
BeautifulSoup(page, "lxml", parse_only=parse_only)