I completely agree with Shrike. I would definitely wait until Spring before forcing your poor cat outside. Once you and your family are outside too the cat will enjoy being out there and will gradually gain enough confidence to go out by itself via a cat flap. I love cat flaps because they allow cats to make their own choices on where they want to be.
My first cat started going outside at quite a young age, once she had been fully vaccinated, but I made sure I was outside with her and it was at Autumn time so the weather was mild. I installed a cat flap once she had been neutered but it took a good few weeks before she would use it when I wasn't at home. One of my current cats was 'forced' outside by his original owner every night with the cat flap locked - once I took him I gave him free choice to do what he wanted and he became more or less a house cat with just brief forays outside to toilet, he has no interest in exploring or hunting. He probably has bad memories of when he was forced outside. I have 3 cats in total now and only one of them spends more than about 10 minutes outside at this time of year though they all obviously like to be outside, for much longer periods, when the weather is warm, the doors are open and I am in and out of the garden myself.
So, definitely wait until the weather warms up and never force the cat outside, let it want to follow you outside and then spend some time outside yourself, perhaps playing a bit (I use twigs for my cats to chase). You need to make the outdoors a pleasurable experience for your poor little cat, who at only 5 months, is still a baby.