England hit their UEFA U-19 Elite Round qualifying group hosts Serbia for six but must win the group decider against Germany on Monday morning to reach the finals.
Jessica Ngunga put the Young Lionesses on the path to victory, with a five-minute brace inside the first quarter of the match.
Hannah Cain then added a third goal, with still less than half an hour played in Senec.
Florence Allen further extended the lead after the hour mark, with Ella Toone converting a penalty and Shania Hayles coming off the bench to complete the scoring.
Despite the big victory, Rehanne Skinner’s side still trail Germany on goal-difference, so will need to defeat them to win the group and reach the finals.
Germany earlier won their second match 3-0 over Israel, with Lea Schneider and Kristin Meyer scoring in the first quarter of an hour and substitute Anna-Lena Stolze getting the third midway through the second half.
England U-19s: Emily Ramsey, Florence Allen, Poppy Pattinson, Esme Morgan, Hannah Cain, Constance Schofield (Jessica Jones, 69), Lauren Hemp, Ella Toone (C) (Shania Hayles, 79), Jessica Ngunga (Aimee Palmer, 87), Rebecca Rayner, Georgia Eaton-Collins
Unused Subs: Katie Startup, Hollie Olding, Olivia Smith, Bridget Galloway, Amy Rodgers, Grace Smith