The Athlon 5350 would be more than adequate for office applications, it's not a low-end processor by any means. My father still utilises his laptop with a Core 2 Duo for office work, and to be honest since it has a SSD it performs better than my current setup (my setup is by no means high-end, it was actually a budget build.) Even without the SSD, even weaker processors than the Core 2 Duo (T9300) are satisfactory for office work; I used a Pentium 4 throughout high school and college (2005-2012) for office work daily. It was NOT a socket 775 P4 either, it was on 478 with a small regular HDD.
The Athlon 5350 in my opinion would still be decent at running games at medium graphical setting, depending on your discrete GPU. For the performance and price of the Athlon 5350, it's a decent worthwhile processor. However for $15 more (not including motherboard or other component costs), the Pentium is a better investment.
Whether you are deciding on purchasing the Intel or AMD, I'd consider if you're going to be installing a dedicated GPU or not. If not, then the Athlon does provide a better graphical performance.
Regardless, I think that you may receive more "fun" from the Intel Pentium; of course that is subjective and is down to opinion. You may prefer the Athlon, whereas I may prefer the Pentium or vice versa. I agree with Rakeen however, try overclocking your Pentium as much as you can to get a decent kick out of it; go the extra mile and even try for 5GHz. Tied with a GPU, see if you can load more recent games at medium-high graphical setting. Of course for more "fun" you could look into water cooling rather than air/prebundled watercoolers.
You're fine with the H81 motherboard, as I'm sure you're aware of what you're doing, however I would completely recommend a Z87/97 motherboard if you don't already have a motherboard.
All the best.