rocknbil - 4:56 pm on Feb 25, 2011 (gmt 0) [edited by: rocknbil at 5:00 pm (utc) on Feb 25, 2011]
^ ^ ^ That would be the way to go, but if this is the result of some theme and is output dynamically, here's a couple other ideas to go with.
The table HTML is horribly broken, 1) there is an opening second table tag that is never closed, 2) you can't use an <h1> element as a table attribute, 3) there is no closing > for the table tag, 4) there is no row declaration for the following td, 5) you can't have anything between the table, tr, or td (except comments) - all that markup needs to go inside a table cell, 6) a table is not valid inside a <p>, 7) there is a mixure of HTML and XHTML break tags, choose one or the other depending on your document type. The font tag has been long deprecated, but it will still "work" if it's moved inside the td.
Compare this valid and simplified version of a table with yours and see what's different.
<p> </p><!-- this is bad, using empty elements for visual effects, but it's valid. -->
<table border="5px" bgcolor="#333333" bordercolor="#000000" title="my title">
<tr> <!-- start a table row -->
<font size="6.5" color="#FFFFFF" face="Book Antiqua">My<br>
<font size="2.5" color="#CBCBCB" face="VERDANA">
these are the things we do
<font size="7" color="#FFFFFF" face="Book Antiqua">my<br></font>
<font size="3.5" color="#FFFFFF" face="Book Antiqua">logo</font>
<font size="3" color="#FFFFFF" face="VERDANA">my contact info
</tr> <!-- end the table row -->
Take note of pairs - there are only a few elements (<hr>, <br>, <img>, etc.) that do not require closing tags.
<table> and </table>
<tr> and </tr>
<td> and </td>
<p> and </p>
It's still a bad approach, but until you get up to speed with table-less layout and CSS, it will ""work" and will probably fix your border problem.
[edited by: rocknbil at 5:00 pm (utc) on Feb 25, 2011]