Forecasting variance (several time steps ahead)

Suppose I'm modeling a daily time series --let's say it's a random walk with drift and I'm using an ARIMA model-- and I want to do a forecast. Let's label today as 'time T' and suppose I want to forecast 5 days out, so 'T+5'. I'm not really interested in the point estimate of the forecast, rather I'm interested in probability distribution of the forecast and I want to obtain the variance for T+5. I can build a model and obtain a point estimate and variance for a day ahead (T+1). Is there a way take the variance predicted for T+1 and get the variance for, T+5? It seems like the further out in the future we try to predict, the wider the variance will be...but how do I obtain the variance for different time steps?