It is tough to say what the loss will be to the BND if the 10 year US treasury yield goes up to 5%. The main reason is because the BND is not comprised of just US treasuries. In addition the holdings of the BND fund can change.
------------ What is the BND ------------
The fund employs an indexing investment approach designed to track the performance of the Barclays U.S. Aggregate Float Adjusted Bond Index. This index measures a wide spectrum of public, investment-grade, taxable, fixed income securities in the United States—including government, corporate, and international dollar-denominated bonds, as well as mortgage-backed and asset-backed securities, all with maturities of more than 1 year. The fund invests by sampling the index, meaning that it holds a range of securities that, in the aggregate, approximate the full index in terms of key risk factors and other characteristics...
More information can be found here - Vanguard Total Bond Market ETF
As of 05/31/2012 69.7% of the BND is in U.S. Treasury, U.S. Agency, and U.S. Agency mortgage-backed securities. They do not specify an exact amount in the 10 Year Treasury. - Portfolio composition
------------ Attempting to gauge potential losses ------------
We can try to gauge potential losses by just using some basic analysis.
For this example and to make it simple we will pretend 70% of the fund is in 10 Year Treasuries(IT IS NOT!)
By getting rid of all other variables and just focusing in on the 10 Year it would be logical to assume that for each X amount the 10 Year price decreased 70% of BND would be effected by that same amount.
However 70% of BND is not in 10 Year Treasuries. Also if the yield were to go up we would have to ask -- "Why is it going up?", "How will other debt be affected?", "Will the funds management react? And if so how?"
Another way to assess how BND would be affected by an increase in the 10 Year yield would be to just look at previous situations. We can use charts for that.
^TNX vs BND - Yahoo
(it's important to note that TNX is the value of the yield so if the price is 2.00 then the yield is 2%)
This is a 5 year chart of BND and the yield of the 10 year treasury. From looking at certain time periods we can see how the BND reacts to increases/decreases in the yield.
For example if you look at 12/30/2008 - 6/11/2009 the yield went from 2.08% to just under 4% at which time BND barely nudged.
I suggest looking at the prospectus and additional information provided to understand the risks involved.
Here are the Distributions for BND.