As you probably know already, the 5300A manual is readily available online but the 5303A does not appear to be. However, in November 2015 someone on EEVblog said that Dave of Artek Manuals had made a scan of it for him. It won't be free, but you can buy a copy of the scan from Dave. (He is a ham, NR1DX.)
He does excellent work and has a large number of manual scans available for HP/Agilent, Tektronix and others. (I believe he only does things that are no longer supported by their manufacturers.)
His web site is artekmanuals.com. Quoting from the home page,
"High quality, digital copies of manuals for obsolete test equipment.
Out of date and hard to find technical manuals are our specialty."
If you need some old manual and can't find it online he may have a scan of it. The prices are reasonable and the quality of the scans is good. (Or as good as they can be, depending on the condition of the original paper copies!)
Disclaimer--I have no interest or stake in his business; just a satisfied customer.
