The basic reason is that 5 years is the typical time at which an investor will hope to cash-out of the investment and collect her profits. 

Why?  There could be several factors driving the length of time before an investor cashes-out.  Generally, however, an investor will always expect a very good return on the investment in your new business.  This very good return is justified as compensation for the risk associated with the chance that your business may not succeed.  Because more mature companies tend not to grow as quickly as younger companies, returns in the years #6 and #7 would tend to be lower and would lower the investor's total return (since, mathematically, all years of the investment must "deliver" the same return).  Since the investor wishes to maximize her very good return, she would generally choose to cash-out of her investment at year #5 before the lower performing years #6 and #7 occur.

But as mentioned, there could be several factors which impact the investor's decision when to cash-out.  The thinking above is only one such factor.  Another factor, often encountered if the investor is a Private Equity firm investing the money of others, is that the investor may be legally obligated to exit the investment after a fixed amount of time.  On the other extreme, some angel investors have even said that it's hard enough to predict performance in year #5 let alone 7 years in the future!  Accordingly, they prefer to entirely exclude the last 2 years from their analysis by planning on a cash-out in year #5.

Given the logic above, you might ask:  Why not assume a shorter cash-out period, say 3 years, allowing for the high growth of a very young company to contribute to the investor's very good return?  The answer is because most new companies are still fine tuning their operations after 3 years and a cash-out then would be premature.

Is a 5 year timeframe typical?  Yes

Is it the only time horizon used?  No. Time horizons under and over 5 years are also used, although less common.