Yes, you can. This is what the INDIRECT function is for. You'd just do it this way:
Code:
=VLOOKUP(10,INDIRECT("'Sheet Name'!$B$3:$F$11"),2,FALSE)
(Pause to check for syntax errors....) Yep, I think that's right. The INDIRECT function, as you may have figured out, takes a character string and interprets it as an address or range, which is what you want here. Give it a shot, and let me know if it doesn't work, but I think it's right.