 Nyora kuenderera mberi kweiyi ndima - Mumwaka wa1994-95, Slutskaya akaenderera mberi nekukwira kwake; mushure mekukunda 1995 World Junior zita munaNovember 1994 muBudapest, akatora bronze pa1995 Russian Championships kuti akwanise kupinda mukutanga kwake mukuru ISU Championship. Mumakwikwi eEuropean muna 1995, akadzoka achibva pakudonha mupurogiramu pfupi kuti atange kutamba mutambo wechitatu wakanakisisa wokutamba akasununguka uye akasimuka kuva wechishanu wose. Akakwanisa kupinda mumakwikwi eWorlds pamwe chete nemukundi wesirivha Olga Markova, nekupedza ari pamberi pemukwikwidzi weRussia Maria Butyrskaya 7th. Pa 1995 World Championships, Slutskaya zvakare akawira mupurogiramu pfupi asi akaita matanhatu matatu muchikamu chinotevera, achipedza 5th mupachena skating uye 7th zvachose. 