V5R4M0 upgrade - HMC as well?

[Pete Helgren <Pete@xxxxxxxxxx>]

I am helping a customer prep for a V5R4M0 upgrade from V5R3M0 on a 520.  
They have an HMC and two i5/OS partitions.  They have ordered and 
received the i5/OS upgrade CD's (missing the I_BASE_01 CD as posted 
earlier) but I think I am not done preparing, yet.  I think I need to 
upgrade the HMC as well and the FSP firmware, yes?

The "about" on the HMC shows:

V 4.0
Release 3.3
HMC Build level 20050114.1
MH00224
Backup/Restore fix level (02-17-2005)

Fortunately, fix central has some information about HMC and software 
levels and it looks like the first issue is what HMC level do I want to 
upgrade to.  I assume that I want to go to the latest level (V7 R3.1.0 
?)  Is there a downside to this?  Is there something that requires that 
I upgrade a version at a time?

With the HMC in the mix I am out of my comfort zone a bit.  I just want 
to make sure I include the HMC as part of this upgrade.  Suggestions?  
Resources?

Thanks,

Pete Helgren