My transmission is on its way out on my 180k 2013 ES350. Can I replace it with a 5th gen transmission? Both are 6-Speed U660E Automatic.

 

It appears that it will fit as shown below.
FYI:
Any auto parts junkyard or used parts dealer or even a transmission shop will have access to the database that tells if it fits. It cross references most major components.

I found this on Wikipedia

​​​​​​U660E[edit]6 speed automatic transverse (V6) 6 speed version of the U151E and F

Application:

• 2006-2008 Toyota Previa (V6)
• 2007–2017 Toyota Camry (V6)
• 2007–2018 Lexus ES 350
• 2007–2017 Toyota Aurion (V6)
• 2007–2012 Toyota Blade (V6)
• 2007–2013 Toyota Mark X Zio (V6)
• 2008-2018 Toyota Avalon
• 2009-2017 Toyota Venza
• 2010–2015 Lexus RX350
• 2011-2016 Toyota Sienna
• 2012- Lotus Evora ("IPS")